Primality by Wilson's theorem: Difference between revisions
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The Wilson's theorem method is better suited for computing single primes, as the SoE method causes one to compute all the primes up to the desired item. In this C# implementation, a running factorial is maintained to help the Wilson's theorem method be a little more efficient. The stand-alone results show that when having to compute a BigInteger factorial for every primality test, the performance drops off considerably more. The last performance figure illustrates that memoizing the factorials can help when calculating nearby prime numbers.
=={{header|C++}}==
<lang cpp>#include <iomanip>
#include <iostream>
int factorial_mod(int n, int p) {
unsigned int f = 1;
for (; n > 0; --n) {
f = (f * n) % p;
if (f == 0)
break;
}
return f;
}
bool is_prime(int p) {
return p > 1 && factorial_mod(p - 1, p) == p - 1;
}
int main() {
std::cout << " n | prime?\n------------\n";
std::cout << std::boolalpha;
for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659})
std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n';
std::cout << "\nFirst 120 primes by Wilson's theorem:\n";
int n = 0, p = 1;
for (; n < 120; ++p) {
if (is_prime(p))
std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' ');
}
std::cout << "\n1000th through 1015th primes:\n";
for (int i = 0; n < 1015; ++p) {
if (is_prime(p)) {
if (++n >= 1000)
std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' ');
}
}
}</lang>
{{out}}
<pre>
n | prime?
------------
2 | true
3 | true
9 | false
15 | false
29 | true
37 | true
47 | true
57 | false
67 | true
77 | false
87 | false
97 | true
237 | false
409 | true
659 | true
First 120 primes by Wilson's theorem:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659
1000th through 1015th primes:
7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 8081
</pre>
=={{header|Common Lisp}}==
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