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https://github.com/uutils/coreutils
synced 2024-12-17 08:33:24 +00:00
ff24d48e73
This change does the following: 1. Updates the arithmetic functions in `src/factor/numeric.rs` to correctly handle all cases up to 2^64. When numbers are larger than 2^63, we fall back to slightly slower routines that check for and handle overflow. 2. Since the arithmetic functions will now not overflow, we no longer need the safety net trial division implementation. We now always use Pollard's rho after eliminating small (<=13 bit) primes. 3. Slight tweak in `src/factor/gen_table.rs` to generate the first 1027 primes, which means we test every prime of 13 or fewer bits before going into Pollard's rho. Includes corresponding update in `src/factor/prime_table.rs` and the Makefile to reflect this. 4. Add a new test that generates random numbers with exclusively large (14 to 50 bit) prime factors. This exercises the possible overflow paths. 5. Add another new test that checks the `is_prime()` function against a few dozen 64-bit primes. Again this is to exercise possible overflow paths.
536 lines
30 KiB
Rust
536 lines
30 KiB
Rust
/*
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* This file is part of the uutils coreutils package.
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*
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* (c) kwantam <kwantam@gmail.com>
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*
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* For the full copyright and license information, please view the LICENSE file
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* that was distributed with this source code.
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*/
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extern crate libc;
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extern crate rand;
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use rand::{weak_rng, Rng};
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use rand::distributions::{IndependentSample, Range};
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use sieve::Sieve;
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use std::io::Write;
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use std::process::{Command, Stdio};
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#[path="../src/factor/sieve.rs"]
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mod sieve;
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const NUM_PRIMES: usize = 10000;
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const LOG_PRIMES: f64 = 14.0; // ceil(log2(NUM_PRIMES))
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const NUM_TESTS: usize = 1000;
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const PROGNAME: &'static str = "./factor";
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#[test]
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fn test_random() {
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let mut primes = Sieve::new().take(NUM_PRIMES - 1).collect::<Vec<u64>>();
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primes.push(2);
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let primes = primes;
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let mut rng = weak_rng();
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let mut rand_gt = move |min: u64| {
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let mut product = 1u64;
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let mut factors = Vec::new();
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while product < min {
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// log distribution---higher probability for lower numbers
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let mut factor;
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loop {
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let next = rng.gen_range(0f64, LOG_PRIMES).exp2().floor() as usize;
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if next < NUM_PRIMES {
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factor = primes[next];
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break;
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}
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}
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let factor = factor;
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match product.checked_mul(factor) {
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Some(p) => {
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product = p;
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factors.push(factor);
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},
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None => break,
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};
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}
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factors.sort();
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(product, factors)
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};
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// build an input and expected output string from factor
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let mut instring = String::new();
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let mut outstring = String::new();
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for _ in 0..NUM_TESTS {
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let (product, factors) = rand_gt(1 << 63);
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instring.push_str(&(format!("{} ", product))[..]);
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outstring.push_str(&(format!("{}:", product))[..]);
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for factor in factors {
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outstring.push_str(&(format!(" {}", factor))[..]);
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}
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outstring.push_str("\n");
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}
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run(instring.as_bytes(), outstring.as_bytes());
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}
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#[test]
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fn test_random_big() {
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let mut rng = weak_rng();
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let bitrange_1 = Range::new(14usize, 51);
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let mut rand_64 = move || {
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// first, choose a random number of bits for the first factor
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let f_bit_1 = bitrange_1.ind_sample(&mut rng);
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// how many more bits do we need?
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let rem = 64 - f_bit_1;
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// we will have a number of additional factors equal to nfacts + 1
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// where nfacts is in [0, floor(rem/14) ) NOTE half-open interval
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// Each prime factor is at least 14 bits, hence floor(rem/14)
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let nfacts = Range::new(0usize, rem / 14).ind_sample(&mut rng);
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// we have to distribute extrabits among the (nfacts + 1) values
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let extrabits = rem - (nfacts + 1) * 14;
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// (remember, a Range is a half-open interval)
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let extrarange = Range::new(0usize, extrabits + 1);
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// to generate an even split of this range, generate n-1 random elements
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// in the range, add the desired total value to the end, sort this list,
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// and then compute the sequential differences.
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let mut f_bits = Vec::new();
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for _ in 0..nfacts {
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f_bits.push(extrarange.ind_sample(&mut rng));
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}
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f_bits.push(extrabits);
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f_bits.sort();
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// compute sequential differences here. We leave off the +14 bits
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// so we can just index PRIMES_BY_BITS
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let mut f_bits = f_bits.iter().scan(0, |st,&x| {
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let ret = x - *st; // + 14 would give actual number of bits
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*st = x;
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Some(ret)
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}).collect::<Vec<usize>>();
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// finally, add f_bit_1 in there
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f_bits.push(f_bit_1 - 14); // index of f_bit_1 in PRIMES_BY_BITS
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let f_bits = f_bits;
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let mut nbits = 0;
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let mut product = 1u64;
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let mut factors = Vec::new();
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for bit in f_bits {
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assert!(bit < 37);
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nbits += 14 + bit;
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let elm = Range::new(0, PRIMES_BY_BITS[bit].len()).ind_sample(&mut rng);
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let factor = PRIMES_BY_BITS[bit][elm];
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factors.push(factor);
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product *= factor;
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}
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assert_eq!(nbits, 64);
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factors.sort();
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(product, factors)
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};
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let mut instring = String::new();
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let mut outstring = String::new();
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for _ in 0..NUM_TESTS {
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let (product, factors) = rand_64();
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instring.push_str(&(format!("{} ", product))[..]);
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outstring.push_str(&(format!("{}:", product))[..]);
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for factor in factors {
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outstring.push_str(&(format!(" {}", factor))[..]);
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}
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outstring.push_str("\n");
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}
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run(instring.as_bytes(), outstring.as_bytes());
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}
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#[test]
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fn test_big_primes() {
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let mut instring = String::new();
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let mut outstring = String::new();
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for prime in PRIMES64 {
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instring.push_str(&(format!("{} ", prime))[..]);
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outstring.push_str(&(format!("{0}: {0}\n", prime))[..]);
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}
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run(instring.as_bytes(), outstring.as_bytes());
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}
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fn run(instring: &[u8], outstring: &[u8]) {
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// now run factor
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let mut process = Command::new(PROGNAME)
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.stdin(Stdio::piped())
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.stdout(Stdio::piped())
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.spawn()
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.unwrap_or_else(|e| panic!("{}", e));
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process.stdin.take().unwrap_or_else(|| panic!("Could not take child process stdin"))
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.write_all(instring).unwrap_or_else(|e| panic!("{}", e));
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let output = process.wait_with_output().unwrap_or_else(|e| panic!("{}", e));
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assert_eq!(&output.stdout[..], outstring);
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}
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const PRIMES_BY_BITS: &'static [&'static [u64]] = &[PRIMES14, PRIMES15, PRIMES16, PRIMES17,
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PRIMES18, PRIMES19, PRIMES20, PRIMES21, PRIMES22, PRIMES23, PRIMES24, PRIMES25, PRIMES26,
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PRIMES27, PRIMES28, PRIMES29, PRIMES30, PRIMES31, PRIMES32, PRIMES33, PRIMES34, PRIMES35,
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PRIMES36, PRIMES37, PRIMES38, PRIMES39, PRIMES40, PRIMES41, PRIMES42, PRIMES43, PRIMES44,
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PRIMES45, PRIMES46, PRIMES47, PRIMES48, PRIMES49, PRIMES50,
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];
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const PRIMES64: &'static [u64] = &[18446744073709551557, 18446744073709551533,
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18446744073709551521, 18446744073709551437, 18446744073709551427, 18446744073709551359,
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18446744073709551337, 18446744073709551293, 18446744073709551263, 18446744073709551253,
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18446744073709551191, 18446744073709551163, 18446744073709551113, 18446744073709550873,
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18446744073709550791, 18446744073709550773, 18446744073709550771, 18446744073709550719,
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18446744073709550717, 18446744073709550681, 18446744073709550671, 18446744073709550593,
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18446744073709550591, 18446744073709550539, 18446744073709550537, 18446744073709550381,
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18446744073709550341, 18446744073709550293, 18446744073709550237, 18446744073709550147,
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18446744073709550141, 18446744073709550129, 18446744073709550111, 18446744073709550099,
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18446744073709550047, 18446744073709550033, 18446744073709550009, 18446744073709549951,
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18446744073709549861, 18446744073709549817, 18446744073709549811, 18446744073709549777,
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18446744073709549757, 18446744073709549733, 18446744073709549667, 18446744073709549621,
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18446744073709549613, 18446744073709549583, 18446744073709549571,
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];
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const PRIMES14: &'static [u64] = &[16381, 16369, 16363, 16361, 16349, 16339, 16333, 16319,
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16301, 16273, 16267, 16253, 16249, 16231, 16229, 16223, 16217, 16193, 16189, 16187, 16183,
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16141, 16139, 16127, 16111, 16103, 16097, 16091, 16087, 16073, 16069, 16067, 16063, 16061,
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16057, 16033, 16007, 16001, 15991, 15973, 15971, 15959, 15937, 15923, 15919, 15913, 15907,
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15901, 15889, 15887, 15881, 15877, 15859, 15823, 15817, 15809, 15803, 15797, 15791, 15787,
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15773, 15767, 15761, 15749, 15739, 15737, 15733, 15731, 15727, 15683, 15679, 15671, 15667,
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15661, 15649, 15647, 15643, 15641, 15629, 15619, 15607, 15601, 15583, 15581, 15569, 15559,
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15551, 15541, 15527, 15511, 15497, 15493, 15473, 15467, 15461, 15451, 15443, 15439, 15427,
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15413, 15401, 15391, 15383, 15377, 15373,
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];
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const PRIMES15: &'static [u64] = &[32749, 32719, 32717, 32713, 32707, 32693, 32687, 32653,
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32647, 32633, 32621, 32611, 32609, 32603, 32587, 32579, 32573, 32569, 32563, 32561, 32537,
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32533, 32531, 32507, 32503, 32497, 32491, 32479, 32467, 32443, 32441, 32429, 32423, 32413,
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32411, 32401, 32381, 32377, 32371, 32369, 32363, 32359, 32353, 32341, 32327, 32323, 32321,
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32309, 32303, 32299, 32297, 32261, 32257, 32251, 32237, 32233, 32213, 32203, 32191, 32189,
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32183, 32173, 32159, 32143, 32141, 32119, 32117, 32099, 32089, 32083, 32077, 32069, 32063,
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32059, 32057, 32051, 32029, 32027, 32009, 32003, 31991, 31981, 31973, 31963, 31957, 31907,
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31891, 31883, 31873, 31859, 31849, 31847, 31817, 31799, 31793, 31771, 31769, 31751,
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];
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const PRIMES16: &'static [u64] = &[65521, 65519, 65497, 65479, 65449, 65447, 65437, 65423,
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65419, 65413, 65407, 65393, 65381, 65371, 65357, 65353, 65327, 65323, 65309, 65293, 65287,
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65269, 65267, 65257, 65239, 65213, 65203, 65183, 65179, 65173, 65171, 65167, 65147, 65141,
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65129, 65123, 65119, 65111, 65101, 65099, 65089, 65071, 65063, 65053, 65033, 65029, 65027,
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65011, 65003, 64997, 64969, 64951, 64937, 64927, 64921, 64919, 64901, 64891, 64879, 64877,
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64871, 64853, 64849, 64817, 64811, 64793, 64783, 64781, 64763, 64747, 64717, 64709, 64693,
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64679, 64667, 64663, 64661, 64633, 64627, 64621, 64613, 64609, 64601, 64591, 64579, 64577,
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64567, 64553,
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];
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const PRIMES17: &'static [u64] = &[131071, 131063, 131059, 131041, 131023, 131011, 131009,
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130987, 130981, 130973, 130969, 130957, 130927, 130873, 130859, 130843, 130841, 130829,
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130817, 130811, 130807, 130787, 130783, 130769, 130729, 130699, 130693, 130687, 130681,
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130657, 130651, 130649, 130643, 130639, 130633, 130631, 130621, 130619, 130589, 130579,
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130553, 130547, 130531, 130523, 130517, 130513, 130489, 130483, 130477, 130469, 130457,
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130447, 130439, 130423, 130411, 130409, 130399, 130379, 130369, 130367, 130363, 130349,
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130343, 130337, 130307, 130303, 130279, 130267, 130261, 130259, 130253, 130241, 130223,
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130211, 130201, 130199, 130183, 130171, 130147, 130127, 130121, 130099, 130087, 130079,
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130073, 130069, 130057, 130051,
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];
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const PRIMES18: &'static [u64] = &[262139, 262133, 262127, 262121, 262111, 262109, 262103,
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262079, 262069, 262051, 262049, 262027, 262007, 261983, 261977, 261973, 261971, 261959,
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261917, 261887, 261881, 261847, 261823, 261799, 261791, 261787, 261773, 261761, 261757,
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261739, 261721, 261713, 261707, 261697, 261673, 261643, 261641, 261637, 261631, 261619,
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261601, 261593, 261587, 261581, 261577, 261563, 261557, 261529, 261523, 261509, 261467,
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261463, 261451, 261439, 261433, 261431, 261427, 261407, 261389, 261379, 261353, 261347,
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261337, 261329, 261323, 261301, 261281, 261271, 261251, 261241, 261229, 261223, 261169,
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261167, 261127,
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];
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const PRIMES19: &'static [u64] = &[524287, 524269, 524261, 524257, 524243, 524231, 524221,
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524219, 524203, 524201, 524197, 524189, 524171, 524149, 524123, 524119, 524113, 524099,
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524087, 524081, 524071, 524063, 524057, 524053, 524047, 523997, 523987, 523969, 523949,
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523937, 523927, 523907, 523903, 523877, 523867, 523847, 523829, 523801, 523793, 523777,
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523771, 523763, 523759, 523741, 523729, 523717, 523681, 523673, 523669, 523667, 523657,
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523639, 523637, 523631, 523603, 523597, 523577, 523573, 523571, 523553, 523543, 523541,
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523519, 523511, 523493, 523489, 523487, 523463, 523459, 523433, 523427, 523417, 523403,
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523387, 523357, 523351, 523349, 523333, 523307, 523297,
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];
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const PRIMES20: &'static [u64] = &[1048573, 1048571, 1048559, 1048549, 1048517, 1048507,
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1048447, 1048433, 1048423, 1048391, 1048387, 1048367, 1048361, 1048357, 1048343, 1048309,
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1048291, 1048273, 1048261, 1048219, 1048217, 1048213, 1048193, 1048189, 1048139, 1048129,
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1048127, 1048123, 1048063, 1048051, 1048049, 1048043, 1048027, 1048013, 1048009, 1048007,
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1047997, 1047989, 1047979, 1047971, 1047961, 1047941, 1047929, 1047923, 1047887, 1047883,
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1047881, 1047859, 1047841, 1047833, 1047821, 1047779, 1047773, 1047763, 1047751, 1047737,
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1047721, 1047713, 1047703, 1047701, 1047691, 1047689, 1047671, 1047667, 1047653, 1047649,
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1047647, 1047589, 1047587, 1047559,
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];
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const PRIMES21: &'static [u64] = &[2097143, 2097133, 2097131, 2097097, 2097091, 2097083,
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2097047, 2097041, 2097031, 2097023, 2097013, 2096993, 2096987, 2096971, 2096959, 2096957,
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2096947, 2096923, 2096911, 2096909, 2096893, 2096881, 2096873, 2096867, 2096851, 2096837,
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2096807, 2096791, 2096789, 2096777, 2096761, 2096741, 2096737, 2096713, 2096693, 2096687,
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2096681, 2096639, 2096629, 2096621, 2096599, 2096597, 2096569, 2096539, 2096533, 2096483,
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2096449, 2096431, 2096429, 2096411, 2096407, 2096401, 2096399, 2096377, 2096357, 2096291,
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2096273, 2096261, 2096233, 2096231, 2096221, 2096209, 2096191, 2096183, 2096147,
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];
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const PRIMES22: &'static [u64] = &[4194301, 4194287, 4194277, 4194271, 4194247, 4194217,
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4194199, 4194191, 4194187, 4194181, 4194173, 4194167, 4194143, 4194137, 4194131, 4194107,
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4194103, 4194023, 4194011, 4194007, 4193977, 4193971, 4193963, 4193957, 4193939, 4193929,
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4193909, 4193869, 4193807, 4193803, 4193801, 4193789, 4193759, 4193753, 4193743, 4193701,
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4193663, 4193633, 4193573, 4193569, 4193551, 4193549, 4193531, 4193513, 4193507, 4193459,
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4193447, 4193443, 4193417, 4193411, 4193393, 4193389, 4193381, 4193377, 4193369, 4193359,
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4193353, 4193327, 4193309, 4193303, 4193297,
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];
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const PRIMES23: &'static [u64] = &[8388593, 8388587, 8388581, 8388571, 8388547, 8388539,
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8388473, 8388461, 8388451, 8388449, 8388439, 8388427, 8388421, 8388409, 8388377, 8388371,
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8388319, 8388301, 8388287, 8388283, 8388277, 8388239, 8388209, 8388187, 8388113, 8388109,
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8388091, 8388071, 8388059, 8388019, 8388013, 8387999, 8387993, 8387959, 8387957, 8387947,
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8387933, 8387921, 8387917, 8387891, 8387879, 8387867, 8387861, 8387857, 8387839, 8387831,
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8387809, 8387807, 8387741, 8387737, 8387723, 8387707, 8387671, 8387611, 8387609, 8387591,
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];
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const PRIMES24: &'static [u64] = &[16777213, 16777199, 16777183, 16777153, 16777141, 16777139,
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16777127, 16777121, 16777099, 16777049, 16777027, 16776989, 16776973, 16776971, 16776967,
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16776961, 16776941, 16776937, 16776931, 16776919, 16776901, 16776899, 16776869, 16776857,
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16776839, 16776833, 16776817, 16776763, 16776731, 16776719, 16776713, 16776691, 16776689,
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16776679, 16776659, 16776631, 16776623, 16776619, 16776607, 16776593, 16776581, 16776547,
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16776521, 16776491, 16776481, 16776469, 16776451, 16776401, 16776391, 16776379, 16776371,
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16776367, 16776343, 16776337, 16776317, 16776313, 16776289, 16776217, 16776211,
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];
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const PRIMES25: &'static [u64] = &[33554393, 33554383, 33554371, 33554347, 33554341, 33554317,
|
|
33554291, 33554273, 33554267, 33554249, 33554239, 33554221, 33554201, 33554167, 33554159,
|
|
33554137, 33554123, 33554093, 33554083, 33554077, 33554051, 33554021, 33554011, 33554009,
|
|
33553999, 33553991, 33553969, 33553967, 33553909, 33553901, 33553879, 33553837, 33553799,
|
|
33553787, 33553771, 33553769, 33553759, 33553747, 33553739, 33553727, 33553697, 33553693,
|
|
33553679, 33553661, 33553657, 33553651, 33553649, 33553633, 33553613, 33553607, 33553577,
|
|
33553549, 33553547, 33553537, 33553519, 33553517, 33553511, 33553489, 33553463, 33553451,
|
|
33553417,
|
|
];
|
|
|
|
const PRIMES26: &'static [u64] = &[67108859, 67108837, 67108819, 67108777, 67108763,
|
|
67108757, 67108753, 67108747, 67108739, 67108729, 67108721, 67108709, 67108693, 67108669,
|
|
67108667, 67108661, 67108649, 67108633, 67108597, 67108579, 67108529, 67108511, 67108507,
|
|
67108493, 67108471, 67108463, 67108453, 67108439, 67108387, 67108373, 67108369, 67108351,
|
|
67108331, 67108313, 67108303, 67108289, 67108271, 67108219, 67108207, 67108201, 67108199,
|
|
67108187, 67108183, 67108177, 67108127, 67108109, 67108081, 67108049, 67108039, 67108037,
|
|
67108033, 67108009, 67108007, 67108003, 67107983, 67107977, 67107967, 67107941, 67107919,
|
|
67107913, 67107883, 67107881, 67107871, 67107863,
|
|
];
|
|
|
|
const PRIMES27: &'static [u64] = &[134217689, 134217649, 134217617, 134217613, 134217593,
|
|
134217541, 134217529, 134217509, 134217497, 134217493, 134217487, 134217467, 134217439,
|
|
134217437, 134217409, 134217403, 134217401, 134217367, 134217361, 134217353, 134217323,
|
|
134217301, 134217277, 134217257, 134217247, 134217221, 134217199, 134217173, 134217163,
|
|
134217157, 134217131, 134217103, 134217089, 134217079, 134217049, 134217047, 134217043,
|
|
134217001, 134216987, 134216947, 134216939, 134216933, 134216911, 134216899, 134216881,
|
|
134216869, 134216867, 134216861, 134216837, 134216827, 134216807, 134216801, 134216791,
|
|
134216783, 134216777, 134216759, 134216737, 134216729,
|
|
];
|
|
|
|
const PRIMES28: &'static [u64] = &[268435399, 268435367, 268435361, 268435337, 268435331,
|
|
268435313, 268435291, 268435273, 268435243, 268435183, 268435171, 268435157, 268435147,
|
|
268435133, 268435129, 268435121, 268435109, 268435091, 268435067, 268435043, 268435039,
|
|
268435033, 268435019, 268435009, 268435007, 268434997, 268434979, 268434977, 268434961,
|
|
268434949, 268434941, 268434937, 268434857, 268434841, 268434827, 268434821, 268434787,
|
|
268434781, 268434779, 268434773, 268434731, 268434721, 268434713, 268434707, 268434703,
|
|
268434697, 268434659, 268434623, 268434619, 268434581, 268434577, 268434563, 268434557,
|
|
268434547, 268434511, 268434499, 268434479, 268434461,
|
|
];
|
|
|
|
const PRIMES29: &'static [u64] = &[536870909, 536870879, 536870869, 536870849, 536870839,
|
|
536870837, 536870819, 536870813, 536870791, 536870779, 536870767, 536870743, 536870729,
|
|
536870723, 536870717, 536870701, 536870683, 536870657, 536870641, 536870627, 536870611,
|
|
536870603, 536870599, 536870573, 536870569, 536870563, 536870561, 536870513, 536870501,
|
|
536870497, 536870473, 536870401, 536870363, 536870317, 536870303, 536870297, 536870273,
|
|
536870267, 536870239, 536870233, 536870219, 536870171, 536870167, 536870153, 536870123,
|
|
536870063, 536870057, 536870041, 536870027, 536869999, 536869951, 536869943, 536869937,
|
|
536869919, 536869901, 536869891,
|
|
];
|
|
|
|
const PRIMES30: &'static [u64] = &[1073741789, 1073741783, 1073741741, 1073741723, 1073741719,
|
|
1073741717, 1073741689, 1073741671, 1073741663, 1073741651, 1073741621, 1073741567, 1073741561,
|
|
1073741527, 1073741503, 1073741477, 1073741467, 1073741441, 1073741419, 1073741399, 1073741387,
|
|
1073741381, 1073741371, 1073741329, 1073741311, 1073741309, 1073741287, 1073741237, 1073741213,
|
|
1073741197, 1073741189, 1073741173, 1073741101, 1073741077, 1073741047, 1073740963, 1073740951,
|
|
1073740933, 1073740909, 1073740879, 1073740853, 1073740847, 1073740819, 1073740807,
|
|
];
|
|
|
|
const PRIMES31: &'static [u64] = &[2147483647, 2147483629, 2147483587, 2147483579, 2147483563,
|
|
2147483549, 2147483543, 2147483497, 2147483489, 2147483477, 2147483423, 2147483399, 2147483353,
|
|
2147483323, 2147483269, 2147483249, 2147483237, 2147483179, 2147483171, 2147483137, 2147483123,
|
|
2147483077, 2147483069, 2147483059, 2147483053, 2147483033, 2147483029, 2147482951, 2147482949,
|
|
2147482943, 2147482937, 2147482921, 2147482877, 2147482873, 2147482867, 2147482859, 2147482819,
|
|
2147482817, 2147482811, 2147482801, 2147482763, 2147482739, 2147482697, 2147482693, 2147482681,
|
|
2147482663, 2147482661,
|
|
];
|
|
|
|
const PRIMES32: &'static [u64] = &[4294967291, 4294967279, 4294967231, 4294967197, 4294967189,
|
|
4294967161, 4294967143, 4294967111, 4294967087, 4294967029, 4294966997, 4294966981, 4294966943,
|
|
4294966927, 4294966909, 4294966877, 4294966829, 4294966813, 4294966769, 4294966667, 4294966661,
|
|
4294966657, 4294966651, 4294966639, 4294966619, 4294966591, 4294966583, 4294966553, 4294966477,
|
|
4294966447, 4294966441, 4294966427, 4294966373, 4294966367, 4294966337, 4294966297,
|
|
];
|
|
|
|
const PRIMES33: &'static [u64] = &[8589934583, 8589934567, 8589934543, 8589934513, 8589934487,
|
|
8589934307, 8589934291, 8589934289, 8589934271, 8589934237, 8589934211, 8589934207, 8589934201,
|
|
8589934187, 8589934151, 8589934141, 8589934139, 8589934117, 8589934103, 8589934099, 8589934091,
|
|
8589934069, 8589934049, 8589934027, 8589934007, 8589933973, 8589933971, 8589933967, 8589933931,
|
|
8589933917, 8589933907, 8589933853, 8589933827, 8589933823, 8589933787, 8589933773, 8589933733,
|
|
8589933731, 8589933721, 8589933683, 8589933647, 8589933641, 8589933637, 8589933631, 8589933629,
|
|
8589933619, 8589933601, 8589933581,
|
|
];
|
|
|
|
const PRIMES34: &'static [u64] = &[17179869143, 17179869107, 17179869071, 17179869053,
|
|
17179869041, 17179869019, 17179868999, 17179868977, 17179868957, 17179868903, 17179868899,
|
|
17179868887, 17179868879, 17179868873, 17179868869, 17179868861, 17179868843, 17179868833,
|
|
17179868809, 17179868807, 17179868777, 17179868759, 17179868729, 17179868711, 17179868683,
|
|
17179868681, 17179868597, 17179868549, 17179868543, 17179868521, 17179868513, 17179868479,
|
|
17179868443, 17179868437, 17179868429, 17179868383, 17179868369, 17179868357, 17179868353,
|
|
17179868351, 17179868333, 17179868317, 17179868309, 17179868297, 17179868287, 17179868249,
|
|
17179868243, 17179868183,
|
|
];
|
|
|
|
const PRIMES35: &'static [u64] = &[34359738337, 34359738319, 34359738307, 34359738299,
|
|
34359738289, 34359738247, 34359738227, 34359738121, 34359738059, 34359738043, 34359738011,
|
|
34359737917, 34359737869, 34359737849, 34359737837, 34359737821, 34359737813, 34359737791,
|
|
34359737777, 34359737771, 34359737717, 34359737591, 34359737567, 34359737549, 34359737519,
|
|
34359737497, 34359737479, 34359737407, 34359737393, 34359737371,
|
|
];
|
|
|
|
const PRIMES36: &'static [u64] = &[68719476731, 68719476719, 68719476713, 68719476671,
|
|
68719476619, 68719476599, 68719476577, 68719476563, 68719476547, 68719476503, 68719476493,
|
|
68719476479, 68719476433, 68719476407, 68719476391, 68719476389, 68719476377, 68719476361,
|
|
68719476323, 68719476307, 68719476281, 68719476271, 68719476257, 68719476247, 68719476209,
|
|
68719476197, 68719476181, 68719476169, 68719476157, 68719476149, 68719476109, 68719476053,
|
|
68719476047, 68719476019, 68719475977, 68719475947, 68719475933, 68719475911, 68719475893,
|
|
68719475879, 68719475837, 68719475827, 68719475809, 68719475791, 68719475779, 68719475771,
|
|
68719475767, 68719475731, 68719475729,
|
|
];
|
|
|
|
const PRIMES37: &'static [u64] = &[137438953447, 137438953441, 137438953427, 137438953403,
|
|
137438953349, 137438953331, 137438953273, 137438953271, 137438953121, 137438953097,
|
|
137438953037, 137438953009, 137438952953, 137438952901, 137438952887, 137438952869,
|
|
137438952853, 137438952731, 137438952683, 137438952611, 137438952529, 137438952503,
|
|
137438952491,
|
|
];
|
|
|
|
const PRIMES38: &'static [u64] = &[274877906899, 274877906857, 274877906837, 274877906813,
|
|
274877906791, 274877906759, 274877906753, 274877906717, 274877906713, 274877906687,
|
|
274877906647, 274877906629, 274877906627, 274877906573, 274877906543, 274877906491,
|
|
274877906477, 274877906473, 274877906431, 274877906419, 274877906341, 274877906333,
|
|
274877906327, 274877906321, 274877906309, 274877906267, 274877906243, 274877906213,
|
|
274877906209, 274877906203, 274877906179, 274877906167, 274877906119, 274877906063,
|
|
274877906053, 274877906021, 274877905931,
|
|
];
|
|
|
|
const PRIMES39: &'static [u64] = &[549755813881, 549755813869, 549755813821, 549755813797,
|
|
549755813753, 549755813723, 549755813669, 549755813657, 549755813647, 549755813587,
|
|
549755813561, 549755813513, 549755813507, 549755813461, 549755813417, 549755813401,
|
|
549755813371, 549755813359, 549755813357, 549755813351, 549755813339, 549755813317,
|
|
549755813311, 549755813281, 549755813239, 549755813231, 549755813213, 549755813207,
|
|
549755813197, 549755813183, 549755813161, 549755813149, 549755813147, 549755813143,
|
|
549755813141, 549755813059, 549755813027, 549755813003, 549755812951, 549755812937,
|
|
549755812933, 549755812889, 549755812867,
|
|
];
|
|
|
|
const PRIMES40: &'static [u64] = &[1099511627689, 1099511627609, 1099511627581, 1099511627573,
|
|
1099511627563, 1099511627491, 1099511627483, 1099511627477, 1099511627387, 1099511627339,
|
|
1099511627321, 1099511627309, 1099511627297, 1099511627293, 1099511627261, 1099511627213,
|
|
1099511627191, 1099511627177, 1099511627173, 1099511627143, 1099511627089, 1099511626987,
|
|
1099511626949, 1099511626937, 1099511626793, 1099511626781, 1099511626771,
|
|
];
|
|
|
|
const PRIMES41: &'static [u64] = &[2199023255531, 2199023255521, 2199023255497, 2199023255489,
|
|
2199023255479, 2199023255477, 2199023255461, 2199023255441, 2199023255419, 2199023255413,
|
|
2199023255357, 2199023255327, 2199023255291, 2199023255279, 2199023255267, 2199023255243,
|
|
2199023255203, 2199023255171, 2199023255137, 2199023255101, 2199023255087, 2199023255081,
|
|
2199023255069, 2199023255027, 2199023255021, 2199023254979, 2199023254933, 2199023254913,
|
|
2199023254907, 2199023254903, 2199023254843, 2199023254787, 2199023254699, 2199023254693,
|
|
2199023254657, 2199023254567,
|
|
];
|
|
|
|
const PRIMES42: &'static [u64] = &[4398046511093, 4398046511087, 4398046511071, 4398046511051,
|
|
4398046511039, 4398046510961, 4398046510943, 4398046510939, 4398046510889, 4398046510877,
|
|
4398046510829, 4398046510787, 4398046510771, 4398046510751, 4398046510733, 4398046510721,
|
|
4398046510643, 4398046510639, 4398046510597, 4398046510577, 4398046510547, 4398046510531,
|
|
4398046510463, 4398046510397, 4398046510391, 4398046510379, 4398046510357, 4398046510331,
|
|
4398046510327, 4398046510313, 4398046510283, 4398046510279, 4398046510217, 4398046510141,
|
|
4398046510133, 4398046510103, 4398046510093,
|
|
];
|
|
|
|
const PRIMES43: &'static [u64] = &[8796093022151, 8796093022141, 8796093022091, 8796093022033,
|
|
8796093021953, 8796093021941, 8796093021917, 8796093021899, 8796093021889, 8796093021839,
|
|
8796093021803, 8796093021791, 8796093021769, 8796093021763, 8796093021743, 8796093021671,
|
|
8796093021607, 8796093021587, 8796093021533, 8796093021523, 8796093021517, 8796093021493,
|
|
8796093021467, 8796093021461, 8796093021449, 8796093021409, 8796093021407, 8796093021371,
|
|
8796093021347, 8796093021337, 8796093021281, 8796093021269,
|
|
];
|
|
|
|
const PRIMES44: &'static [u64] = &[17592186044399, 17592186044299, 17592186044297, 17592186044287,
|
|
17592186044273, 17592186044267, 17592186044129, 17592186044089, 17592186044057, 17592186044039,
|
|
17592186043987, 17592186043921, 17592186043889, 17592186043877, 17592186043841, 17592186043829,
|
|
17592186043819, 17592186043813, 17592186043807, 17592186043741, 17592186043693, 17592186043667,
|
|
17592186043631, 17592186043591, 17592186043577, 17592186043547, 17592186043483, 17592186043451,
|
|
17592186043433, 17592186043409,
|
|
];
|
|
|
|
const PRIMES45: &'static [u64] = &[35184372088777, 35184372088763, 35184372088751, 35184372088739,
|
|
35184372088711, 35184372088699, 35184372088693, 35184372088673, 35184372088639, 35184372088603,
|
|
35184372088571, 35184372088517, 35184372088493, 35184372088471, 35184372088403, 35184372088391,
|
|
35184372088379, 35184372088363, 35184372088321, 35184372088319, 35184372088279, 35184372088259,
|
|
35184372088249, 35184372088241, 35184372088223, 35184372088183, 35184372088097, 35184372088081,
|
|
35184372088079, 35184372088051, 35184372088043, 35184372088039, 35184372087937, 35184372087929,
|
|
35184372087923, 35184372087881, 35184372087877, 35184372087869,
|
|
];
|
|
|
|
const PRIMES46: &'static [u64] = &[70368744177643, 70368744177607, 70368744177601, 70368744177587,
|
|
70368744177497, 70368744177467, 70368744177427, 70368744177377, 70368744177359, 70368744177353,
|
|
70368744177331, 70368744177289, 70368744177283, 70368744177271, 70368744177257, 70368744177227,
|
|
70368744177167, 70368744177113, 70368744177029, 70368744176959, 70368744176921, 70368744176909,
|
|
70368744176879, 70368744176867, 70368744176833, 70368744176827, 70368744176807, 70368744176779,
|
|
70368744176777, 70368744176729, 70368744176719, 70368744176711,
|
|
];
|
|
|
|
const PRIMES47: &'static [u64] = &[140737488355213, 140737488355201, 140737488355181,
|
|
140737488355049, 140737488355031, 140737488354989, 140737488354893, 140737488354787,
|
|
140737488354709, 140737488354679, 140737488354613, 140737488354557, 140737488354511,
|
|
140737488354431, 140737488354413, 140737488354409, 140737488354373, 140737488354347,
|
|
140737488354329,
|
|
];
|
|
|
|
const PRIMES48: &'static [u64] = &[281474976710597, 281474976710591, 281474976710567,
|
|
281474976710563, 281474976710509, 281474976710491, 281474976710467, 281474976710423,
|
|
281474976710413, 281474976710399, 281474976710339, 281474976710327, 281474976710287,
|
|
281474976710197, 281474976710143, 281474976710131, 281474976710129, 281474976710107,
|
|
281474976710089, 281474976710087, 281474976710029, 281474976709987, 281474976709891,
|
|
281474976709859, 281474976709831, 281474976709757, 281474976709741, 281474976709711,
|
|
281474976709649, 281474976709637,
|
|
];
|
|
|
|
const PRIMES49: &'static [u64] = &[562949953421231, 562949953421201, 562949953421189,
|
|
562949953421173, 562949953421131, 562949953421111, 562949953421099, 562949953421047,
|
|
562949953421029, 562949953420973, 562949953420871, 562949953420867, 562949953420837,
|
|
562949953420793, 562949953420747, 562949953420741, 562949953420733, 562949953420727,
|
|
562949953420609, 562949953420571, 562949953420559, 562949953420553, 562949953420523,
|
|
562949953420507, 562949953420457, 562949953420403, 562949953420373, 562949953420369,
|
|
562949953420343, 562949953420303, 562949953420297,
|
|
];
|
|
|
|
const PRIMES50: &'static [u64] = &[1125899906842597, 1125899906842589, 1125899906842573,
|
|
1125899906842553, 1125899906842511, 1125899906842507, 1125899906842493, 1125899906842463,
|
|
1125899906842429, 1125899906842391, 1125899906842357, 1125899906842283, 1125899906842273,
|
|
1125899906842247, 1125899906842201, 1125899906842177, 1125899906842079, 1125899906842033,
|
|
1125899906842021, 1125899906842013, 1125899906841973, 1125899906841971, 1125899906841959,
|
|
1125899906841949, 1125899906841943, 1125899906841917, 1125899906841901, 1125899906841883,
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1125899906841859, 1125899906841811, 1125899906841803, 1125899906841751, 1125899906841713,
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1125899906841673, 1125899906841653, 1125899906841623, 1125899906841613,
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];
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