Fermat pseudoprimes: Difference between revisions
Added C++ solution
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base 19 to 50000 total: 93, first: 6 9 15 18 45 49 153 169 343 561 637 889 905 906 1035 1105 1629 1661 1849 1891
base 20 to 50000 total: 66, first: 21 57 133 231 399 561 671 861 889 1281 1653 1729 1891 2059 2413 2501 2761 2821 2947 3059
</pre>
=={{header|C++}}==
{{trans|Wren}}
<syntaxhighlight lang="cpp">#include <cstdint>
#include <iomanip>
#include <iostream>
uint64_t modpow(uint64_t base, uint64_t exp, uint64_t mod) {
if (mod == 1)
return 0;
uint64_t result = 1;
base %= mod;
for (; exp > 0; exp >>= 1) {
if ((exp & 1) == 1)
result = (result * base) % mod;
base = (base * base) % mod;
}
return result;
}
bool is_prime(uint64_t n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (uint64_t p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}
bool is_fermat_pseudoprime(uint64_t a, uint64_t x) {
return !is_prime(x) && modpow(a, x - 1, x) == 1;
}
int main() {
std::cout << "First 20 Fermat pseudoprimes:\n";
for (uint64_t a = 1; a <= 20; ++a) {
std::cout << "Base " << std::setw(2) << a << ": ";
int count = 0;
for (uint64_t x = 4; count < 20; ++x) {
if (is_fermat_pseudoprime(a, x)) {
++count;
std::cout << std::setw(5) << x << ' ';
}
}
std::cout << '\n';
}
const uint64_t limits[] = {12000, 25000, 50000, 100000};
std::cout << "\nCount <= ";
for (uint64_t limit : limits) {
std::cout << std::setw(6) << limit << ' ';
}
std::cout << "\n------------------------------------\n";
for (uint64_t a = 1; a <= 20; ++a) {
std::cout << "Base " << std::setw(2) << a << ": ";
int count = 0;
uint64_t x = 4;
for (uint64_t limit : limits) {
for (; x <= limit; ++x) {
if (is_fermat_pseudoprime(a, x))
++count;
}
std::cout << std::setw(6) << count << ' ';
}
std::cout << '\n';
}
}</syntaxhighlight>
{{out}}
<pre>
First 20 Fermat pseudoprimes:
Base 1: 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30 32
Base 2: 341 561 645 1105 1387 1729 1905 2047 2465 2701 2821 3277 4033 4369 4371 4681 5461 6601 7957 8321
Base 3: 91 121 286 671 703 949 1105 1541 1729 1891 2465 2665 2701 2821 3281 3367 3751 4961 5551 6601
Base 4: 15 85 91 341 435 451 561 645 703 1105 1247 1271 1387 1581 1695 1729 1891 1905 2047 2071
Base 5: 4 124 217 561 781 1541 1729 1891 2821 4123 5461 5611 5662 5731 6601 7449 7813 8029 8911 9881
Base 6: 35 185 217 301 481 1105 1111 1261 1333 1729 2465 2701 2821 3421 3565 3589 3913 4123 4495 5713
Base 7: 6 25 325 561 703 817 1105 1825 2101 2353 2465 3277 4525 4825 6697 8321 10225 10585 10621 11041
Base 8: 9 21 45 63 65 105 117 133 153 231 273 341 481 511 561 585 645 651 861 949
Base 9: 4 8 28 52 91 121 205 286 364 511 532 616 671 697 703 946 949 1036 1105 1288
Base 10: 9 33 91 99 259 451 481 561 657 703 909 1233 1729 2409 2821 2981 3333 3367 4141 4187
Base 11: 10 15 70 133 190 259 305 481 645 703 793 1105 1330 1729 2047 2257 2465 2821 4577 4921
Base 12: 65 91 133 143 145 247 377 385 703 1045 1099 1105 1649 1729 1885 1891 2041 2233 2465 2701
Base 13: 4 6 12 21 85 105 231 244 276 357 427 561 1099 1785 1891 2465 2806 3605 5028 5149
Base 14: 15 39 65 195 481 561 781 793 841 985 1105 1111 1541 1891 2257 2465 2561 2665 2743 3277
Base 15: 14 341 742 946 1477 1541 1687 1729 1891 1921 2821 3133 3277 4187 6541 6601 7471 8701 8911 9073
Base 16: 15 51 85 91 255 341 435 451 561 595 645 703 1105 1247 1261 1271 1285 1387 1581 1687
Base 17: 4 8 9 16 45 91 145 261 781 1111 1228 1305 1729 1885 2149 2821 3991 4005 4033 4187
Base 18: 25 49 65 85 133 221 323 325 343 425 451 637 931 1105 1225 1369 1387 1649 1729 1921
Base 19: 6 9 15 18 45 49 153 169 343 561 637 889 905 906 1035 1105 1629 1661 1849 1891
Base 20: 21 57 133 231 399 561 671 861 889 1281 1653 1729 1891 2059 2413 2501 2761 2821 2947 3059
Count <= 12000 25000 50000 100000
------------------------------------
Base 1: 10561 22237 44866 90407
Base 2: 25 38 55 78
Base 3: 25 38 53 78
Base 4: 50 75 111 153
Base 5: 22 35 54 73
Base 6: 31 46 74 104
Base 7: 21 32 49 73
Base 8: 76 110 150 218
Base 9: 55 83 113 164
Base 10: 35 53 65 90
Base 11: 30 41 61 89
Base 12: 35 60 91 127
Base 13: 31 51 68 91
Base 14: 33 51 69 96
Base 15: 22 31 42 70
Base 16: 69 102 145 200
Base 17: 31 44 63 83
Base 18: 46 69 98 134
Base 19: 48 70 93 121
Base 20: 35 49 66 101
</pre>
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