// This file is part of the uutils coreutils package. // // (c) kwantam // // For the full copyright and license information, please view the LICENSE file // that was distributed with this source code. #![allow(clippy::unreadable_literal)] // spell-checker:ignore (methods) hexdigest use crate::common::util::TestScenario; use std::time::{Duration, SystemTime}; #[path = "../../src/uu/factor/sieve.rs"] mod sieve; use self::sieve::Sieve; use rand::distributions::{Distribution, Uniform}; use rand::{rngs::SmallRng, Rng, SeedableRng}; const NUM_PRIMES: usize = 10000; const NUM_TESTS: usize = 100; #[test] fn test_invalid_arg() { new_ucmd!().arg("--definitely-invalid").fails().code_is(1); } #[test] #[cfg(feature = "sort")] fn test_parallel() { use crate::common::util::AtPath; use hex_literal::hex; use sha1::{Digest, Sha1}; use std::{fs::OpenOptions, time::Duration}; use tempfile::TempDir; // factor should only flush the buffer at line breaks let n_integers = 100_000; let mut input_string = String::new(); for i in 0..=n_integers { input_string.push_str(&(format!("{i} "))[..]); } let tmp_dir = TempDir::new().unwrap(); let tmp_dir = AtPath::new(tmp_dir.path()); tmp_dir.touch("output"); let output = OpenOptions::new() .append(true) .open(tmp_dir.plus("output")) .unwrap(); for child in (0..10) .map(|_| { new_ucmd!() .timeout(Duration::from_secs(240)) .set_stdout(output.try_clone().unwrap()) .pipe_in(input_string.clone()) .run_no_wait() }) .collect::>() { child.wait().unwrap().success(); } let result = TestScenario::new(util_name!()) .ccmd("sort") .arg(tmp_dir.plus("output")) .succeeds(); let mut hasher = Sha1::new(); hasher.update(result.stdout()); let hash_check = hasher.finalize(); assert_eq!( hash_check[..], hex!("cc743607c0ff300ff575d92f4ff0c87d5660c393") ); } #[test] fn test_first_1000_integers() { use hex_literal::hex; use sha1::{Digest, Sha1}; let n_integers = 1000; let mut input_string = String::new(); for i in 0..=n_integers { input_string.push_str(&(format!("{i} "))[..]); } println!("STDIN='{input_string}'"); let result = new_ucmd!().pipe_in(input_string.as_bytes()).succeeds(); // `seq 0 1000 | factor | sha1sum` => "c734327bd18b90fca5762f671672b5eda19f7dca" let mut hasher = Sha1::new(); hasher.update(result.stdout()); let hash_check = hasher.finalize(); assert_eq!( hash_check[..], hex!("c734327bd18b90fca5762f671672b5eda19f7dca") ); } #[test] fn test_cli_args() { // Make sure that factor works with CLI arguments as well. new_ucmd!().args(&["3"]).succeeds().stdout_contains("3: 3"); new_ucmd!() .args(&["3", "6", " +9"]) .succeeds() .stdout_contains("3: 3") .stdout_contains("9: 3 3"); } #[test] fn test_random() { use conv::prelude::ValueFrom; let log_num_primes = f64::value_from(NUM_PRIMES).unwrap().log2().ceil(); let primes = Sieve::primes().take(NUM_PRIMES).collect::>(); let rng_seed = SystemTime::now() .duration_since(SystemTime::UNIX_EPOCH) .unwrap() .as_secs(); println!("rng_seed={rng_seed:?}"); let mut rng = SmallRng::seed_from_u64(rng_seed); let mut rand_gt = move |min: u64| { let mut product = 1_u64; let mut factors = Vec::new(); while product < min { // log distribution---higher probability for lower numbers let factor; loop { let next = rng.gen_range(0_f64..log_num_primes).exp2().floor() as usize; if next < NUM_PRIMES { factor = primes[next]; break; } } let factor = factor; match product.checked_mul(factor) { Some(p) => { product = p; factors.push(factor); } None => break, }; } factors.sort_unstable(); (product, factors) }; // build an input and expected output string from factor let mut input_string = String::new(); let mut output_string = String::new(); for _ in 0..NUM_TESTS { let (product, factors) = rand_gt(1 << 63); input_string.push_str(&(format!("{product} "))[..]); output_string.push_str(&(format!("{product}:"))[..]); for factor in factors { output_string.push_str(&(format!(" {factor}"))[..]); } output_string.push('\n'); } run(input_string.as_bytes(), output_string.as_bytes()); } #[test] fn test_random_big() { let rng_seed = SystemTime::now() .duration_since(SystemTime::UNIX_EPOCH) .unwrap() .as_secs(); println!("rng_seed={rng_seed:?}"); let mut rng = SmallRng::seed_from_u64(rng_seed); let bit_range_1 = Uniform::new(14_usize, 51); let mut rand_64 = move || { // first, choose a random number of bits for the first factor let f_bit_1 = bit_range_1.sample(&mut rng); // how many more bits do we need? let rem = 64 - f_bit_1; // we will have a number of additional factors equal to n_facts + 1 // where n_facts is in [0, floor(rem/14) ) NOTE half-open interval // Each prime factor is at least 14 bits, hence floor(rem/14) let n_factors = Uniform::new(0_usize, rem / 14).sample(&mut rng); // we have to distribute extra_bits among the (n_facts + 1) values let extra_bits = rem - (n_factors + 1) * 14; // (remember, a Range is a half-open interval) let extra_range = Uniform::new(0_usize, extra_bits + 1); // to generate an even split of this range, generate n-1 random elements // in the range, add the desired total value to the end, sort this list, // and then compute the sequential differences. let mut f_bits = Vec::new(); for _ in 0..n_factors { f_bits.push(extra_range.sample(&mut rng)); } f_bits.push(extra_bits); f_bits.sort_unstable(); // compute sequential differences here. We leave off the +14 bits // so we can just index PRIMES_BY_BITS let mut f_bits = f_bits .iter() .scan(0, |st, &x| { let ret = x - *st; // + 14 would give actual number of bits *st = x; Some(ret) }) .collect::>(); // finally, add f_bit_1 in there f_bits.push(f_bit_1 - 14); // index of f_bit_1 in PRIMES_BY_BITS let f_bits = f_bits; let mut n_bits = 0; let mut product = 1_u64; let mut factors = Vec::new(); for bit in f_bits { assert!(bit < 37); n_bits += 14 + bit; let elm = Uniform::new(0, PRIMES_BY_BITS[bit].len()).sample(&mut rng); let factor = PRIMES_BY_BITS[bit][elm]; factors.push(factor); product *= factor; } assert_eq!(n_bits, 64); factors.sort_unstable(); (product, factors) }; let mut input_string = String::new(); let mut output_string = String::new(); for _ in 0..NUM_TESTS { let (product, factors) = rand_64(); input_string.push_str(&(format!("{product} "))[..]); output_string.push_str(&(format!("{product}:"))[..]); for factor in factors { output_string.push_str(&(format!(" {factor}"))[..]); } output_string.push('\n'); } run(input_string.as_bytes(), output_string.as_bytes()); } #[test] fn test_big_primes() { let mut input_string = String::new(); let mut output_string = String::new(); for prime in PRIMES64 { input_string.push_str(&(format!("{prime} "))[..]); output_string.push_str(&(format!("{prime}: {prime}\n"))[..]); } run(input_string.as_bytes(), output_string.as_bytes()); } fn run(input_string: &[u8], output_string: &[u8]) { println!("STDIN='{}'", String::from_utf8_lossy(input_string)); println!( "STDOUT(expected)='{}'", String::from_utf8_lossy(output_string) ); // now run factor new_ucmd!() .timeout(Duration::from_secs(240)) .pipe_in(input_string) .run() .stdout_is(String::from_utf8(output_string.to_owned()).unwrap()); } const PRIMES_BY_BITS: &[&[u64]] = &[ PRIMES14, PRIMES15, PRIMES16, PRIMES17, PRIMES18, PRIMES19, PRIMES20, PRIMES21, PRIMES22, PRIMES23, PRIMES24, PRIMES25, PRIMES26, PRIMES27, PRIMES28, PRIMES29, PRIMES30, PRIMES31, PRIMES32, PRIMES33, PRIMES34, PRIMES35, PRIMES36, PRIMES37, PRIMES38, PRIMES39, PRIMES40, PRIMES41, PRIMES42, PRIMES43, PRIMES44, PRIMES45, PRIMES46, PRIMES47, PRIMES48, PRIMES49, PRIMES50, ]; const PRIMES64: &[u64] = &[ 18446744073709551557, 18446744073709551533, 18446744073709551521, 18446744073709551437, 18446744073709551427, 18446744073709551359, 18446744073709551337, 18446744073709551293, 18446744073709551263, 18446744073709551253, 18446744073709551191, 18446744073709551163, 18446744073709551113, 18446744073709550873, 18446744073709550791, 18446744073709550773, 18446744073709550771, 18446744073709550719, 18446744073709550717, 18446744073709550681, 18446744073709550671, 18446744073709550593, 18446744073709550591, 18446744073709550539, 18446744073709550537, 18446744073709550381, 18446744073709550341, 18446744073709550293, 18446744073709550237, 18446744073709550147, 18446744073709550141, 18446744073709550129, 18446744073709550111, 18446744073709550099, 18446744073709550047, 18446744073709550033, 18446744073709550009, 18446744073709549951, 18446744073709549861, 18446744073709549817, 18446744073709549811, 18446744073709549777, 18446744073709549757, 18446744073709549733, 18446744073709549667, 18446744073709549621, 18446744073709549613, 18446744073709549583, 18446744073709549571, ]; const PRIMES14: &[u64] = &[ 16381, 16369, 16363, 16361, 16349, 16339, 16333, 16319, 16301, 16273, 16267, 16253, 16249, 16231, 16229, 16223, 16217, 16193, 16189, 16187, 16183, 16141, 16139, 16127, 16111, 16103, 16097, 16091, 16087, 16073, 16069, 16067, 16063, 16061, 16057, 16033, 16007, 16001, 15991, 15973, 15971, 15959, 15937, 15923, 15919, 15913, 15907, 15901, 15889, 15887, 15881, 15877, 15859, 15823, 15817, 15809, 15803, 15797, 15791, 15787, 15773, 15767, 15761, 15749, 15739, 15737, 15733, 15731, 15727, 15683, 15679, 15671, 15667, 15661, 15649, 15647, 15643, 15641, 15629, 15619, 15607, 15601, 15583, 15581, 15569, 15559, 15551, 15541, 15527, 15511, 15497, 15493, 15473, 15467, 15461, 15451, 15443, 15439, 15427, 15413, 15401, 15391, 15383, 15377, 15373, ]; const PRIMES15: &[u64] = &[ 32749, 32719, 32717, 32713, 32707, 32693, 32687, 32653, 32647, 32633, 32621, 32611, 32609, 32603, 32587, 32579, 32573, 32569, 32563, 32561, 32537, 32533, 32531, 32507, 32503, 32497, 32491, 32479, 32467, 32443, 32441, 32429, 32423, 32413, 32411, 32401, 32381, 32377, 32371, 32369, 32363, 32359, 32353, 32341, 32327, 32323, 32321, 32309, 32303, 32299, 32297, 32261, 32257, 32251, 32237, 32233, 32213, 32203, 32191, 32189, 32183, 32173, 32159, 32143, 32141, 32119, 32117, 32099, 32089, 32083, 32077, 32069, 32063, 32059, 32057, 32051, 32029, 32027, 32009, 32003, 31991, 31981, 31973, 31963, 31957, 31907, 31891, 31883, 31873, 31859, 31849, 31847, 31817, 31799, 31793, 31771, 31769, 31751, ]; const PRIMES16: &[u64] = &[ 65521, 65519, 65497, 65479, 65449, 65447, 65437, 65423, 65419, 65413, 65407, 65393, 65381, 65371, 65357, 65353, 65327, 65323, 65309, 65293, 65287, 65269, 65267, 65257, 65239, 65213, 65203, 65183, 65179, 65173, 65171, 65167, 65147, 65141, 65129, 65123, 65119, 65111, 65101, 65099, 65089, 65071, 65063, 65053, 65033, 65029, 65027, 65011, 65003, 64997, 64969, 64951, 64937, 64927, 64921, 64919, 64901, 64891, 64879, 64877, 64871, 64853, 64849, 64817, 64811, 64793, 64783, 64781, 64763, 64747, 64717, 64709, 64693, 64679, 64667, 64663, 64661, 64633, 64627, 64621, 64613, 64609, 64601, 64591, 64579, 64577, 64567, 64553, ]; const PRIMES17: &[u64] = &[ 131071, 131063, 131059, 131041, 131023, 131011, 131009, 130987, 130981, 130973, 130969, 130957, 130927, 130873, 130859, 130843, 130841, 130829, 130817, 130811, 130807, 130787, 130783, 130769, 130729, 130699, 130693, 130687, 130681, 130657, 130651, 130649, 130643, 130639, 130633, 130631, 130621, 130619, 130589, 130579, 130553, 130547, 130531, 130523, 130517, 130513, 130489, 130483, 130477, 130469, 130457, 130447, 130439, 130423, 130411, 130409, 130399, 130379, 130369, 130367, 130363, 130349, 130343, 130337, 130307, 130303, 130279, 130267, 130261, 130259, 130253, 130241, 130223, 130211, 130201, 130199, 130183, 130171, 130147, 130127, 130121, 130099, 130087, 130079, 130073, 130069, 130057, 130051, ]; const PRIMES18: &[u64] = &[ 262139, 262133, 262127, 262121, 262111, 262109, 262103, 262079, 262069, 262051, 262049, 262027, 262007, 261983, 261977, 261973, 261971, 261959, 261917, 261887, 261881, 261847, 261823, 261799, 261791, 261787, 261773, 261761, 261757, 261739, 261721, 261713, 261707, 261697, 261673, 261643, 261641, 261637, 261631, 261619, 261601, 261593, 261587, 261581, 261577, 261563, 261557, 261529, 261523, 261509, 261467, 261463, 261451, 261439, 261433, 261431, 261427, 261407, 261389, 261379, 261353, 261347, 261337, 261329, 261323, 261301, 261281, 261271, 261251, 261241, 261229, 261223, 261169, 261167, 261127, ]; const PRIMES19: &[u64] = &[ 524287, 524269, 524261, 524257, 524243, 524231, 524221, 524219, 524203, 524201, 524197, 524189, 524171, 524149, 524123, 524119, 524113, 524099, 524087, 524081, 524071, 524063, 524057, 524053, 524047, 523997, 523987, 523969, 523949, 523937, 523927, 523907, 523903, 523877, 523867, 523847, 523829, 523801, 523793, 523777, 523771, 523763, 523759, 523741, 523729, 523717, 523681, 523673, 523669, 523667, 523657, 523639, 523637, 523631, 523603, 523597, 523577, 523573, 523571, 523553, 523543, 523541, 523519, 523511, 523493, 523489, 523487, 523463, 523459, 523433, 523427, 523417, 523403, 523387, 523357, 523351, 523349, 523333, 523307, 523297, ]; const PRIMES20: &[u64] = &[ 1048573, 1048571, 1048559, 1048549, 1048517, 1048507, 1048447, 1048433, 1048423, 1048391, 1048387, 1048367, 1048361, 1048357, 1048343, 1048309, 1048291, 1048273, 1048261, 1048219, 1048217, 1048213, 1048193, 1048189, 1048139, 1048129, 1048127, 1048123, 1048063, 1048051, 1048049, 1048043, 1048027, 1048013, 1048009, 1048007, 1047997, 1047989, 1047979, 1047971, 1047961, 1047941, 1047929, 1047923, 1047887, 1047883, 1047881, 1047859, 1047841, 1047833, 1047821, 1047779, 1047773, 1047763, 1047751, 1047737, 1047721, 1047713, 1047703, 1047701, 1047691, 1047689, 1047671, 1047667, 1047653, 1047649, 1047647, 1047589, 1047587, 1047559, ]; const PRIMES21: &[u64] = &[ 2097143, 2097133, 2097131, 2097097, 2097091, 2097083, 2097047, 2097041, 2097031, 2097023, 2097013, 2096993, 2096987, 2096971, 2096959, 2096957, 2096947, 2096923, 2096911, 2096909, 2096893, 2096881, 2096873, 2096867, 2096851, 2096837, 2096807, 2096791, 2096789, 2096777, 2096761, 2096741, 2096737, 2096713, 2096693, 2096687, 2096681, 2096639, 2096629, 2096621, 2096599, 2096597, 2096569, 2096539, 2096533, 2096483, 2096449, 2096431, 2096429, 2096411, 2096407, 2096401, 2096399, 2096377, 2096357, 2096291, 2096273, 2096261, 2096233, 2096231, 2096221, 2096209, 2096191, 2096183, 2096147, ]; const PRIMES22: &[u64] = &[ 4194301, 4194287, 4194277, 4194271, 4194247, 4194217, 4194199, 4194191, 4194187, 4194181, 4194173, 4194167, 4194143, 4194137, 4194131, 4194107, 4194103, 4194023, 4194011, 4194007, 4193977, 4193971, 4193963, 4193957, 4193939, 4193929, 4193909, 4193869, 4193807, 4193803, 4193801, 4193789, 4193759, 4193753, 4193743, 4193701, 4193663, 4193633, 4193573, 4193569, 4193551, 4193549, 4193531, 4193513, 4193507, 4193459, 4193447, 4193443, 4193417, 4193411, 4193393, 4193389, 4193381, 4193377, 4193369, 4193359, 4193353, 4193327, 4193309, 4193303, 4193297, ]; const PRIMES23: &[u64] = &[ 8388593, 8388587, 8388581, 8388571, 8388547, 8388539, 8388473, 8388461, 8388451, 8388449, 8388439, 8388427, 8388421, 8388409, 8388377, 8388371, 8388319, 8388301, 8388287, 8388283, 8388277, 8388239, 8388209, 8388187, 8388113, 8388109, 8388091, 8388071, 8388059, 8388019, 8388013, 8387999, 8387993, 8387959, 8387957, 8387947, 8387933, 8387921, 8387917, 8387891, 8387879, 8387867, 8387861, 8387857, 8387839, 8387831, 8387809, 8387807, 8387741, 8387737, 8387723, 8387707, 8387671, 8387611, 8387609, 8387591, ]; const PRIMES24: &[u64] = &[ 16777213, 16777199, 16777183, 16777153, 16777141, 16777139, 16777127, 16777121, 16777099, 16777049, 16777027, 16776989, 16776973, 16776971, 16776967, 16776961, 16776941, 16776937, 16776931, 16776919, 16776901, 16776899, 16776869, 16776857, 16776839, 16776833, 16776817, 16776763, 16776731, 16776719, 16776713, 16776691, 16776689, 16776679, 16776659, 16776631, 16776623, 16776619, 16776607, 16776593, 16776581, 16776547, 16776521, 16776491, 16776481, 16776469, 16776451, 16776401, 16776391, 16776379, 16776371, 16776367, 16776343, 16776337, 16776317, 16776313, 16776289, 16776217, 16776211, ]; const PRIMES25: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[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: &[u64] = &[ 140737488355213, 140737488355201, 140737488355181, 140737488355049, 140737488355031, 140737488354989, 140737488354893, 140737488354787, 140737488354709, 140737488354679, 140737488354613, 140737488354557, 140737488354511, 140737488354431, 140737488354413, 140737488354409, 140737488354373, 140737488354347, 140737488354329, ]; const PRIMES48: &[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: &[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: &[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, 1125899906841859, 1125899906841811, 1125899906841803, 1125899906841751, 1125899906841713, 1125899906841673, 1125899906841653, 1125899906841623, 1125899906841613, ];