Fermat pseudoprimes: Difference between revisions
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19 93 6 9 15 18 45 49 153 169 343 561 637 889 905 906 1035 1105 1629 1661 1849 1891
20 66 21 57 133 231 399 561 671 861 889 1281 1653 1729 1891 2059 2413 2501 2761 2821 2947 3059
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=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.List;
import java.util.stream.Collectors;
public final class FermatPseudoprimes {
public static void main(String[] args) {
final int limit = 50_000;
for ( int base = 1; base <= 20; base++ ) {
int count = 0;
List<Integer> firstTwenty = new ArrayList<Integer>();
for ( int number = 4; number <= limit; number++ ) {
if ( isFermatPseudoprime(base, number) ) {
count += 1;
if ( count <= 20 ) {
firstTwenty.addLast(number);
}
}
}
System.out.println("Base " + base + ":");
System.out.println(" The number of Fermat pseudoprimes up to " + limit + ": " + count);
System.out.println(" The first 20: " +
firstTwenty.stream().map(String::valueOf).collect(Collectors.joining(" ")));
}
}
private static boolean isFermatPseudoprime(int base, int number) {
return ! isPrime(number) && moduloPower(base, number - 1, number) == 1;
}
private static long moduloPower(long base, long exponent, long modulus) {
if ( modulus == 1 ) {
return 0;
}
base %= modulus;
long result = 1;
while ( exponent > 0 ) {
if ( ( exponent & 1 ) == 1 ) {
result = ( result * base ) % modulus;
}
base = ( base * base ) % modulus;
exponent >>= 1;
}
return result;
}
private static boolean isPrime(int number) {
if ( number < 2 ) {
return false;
}
if ( number % 2 == 0 ) {
return number == 2;
}
if ( number % 3 == 0 ) {
return number == 3;
}
for ( int p = 5; p * p <= number; p += 4 ) {
if ( number % p == 0 ) {
return false;
}
p += 2;
if ( number % p == 0 ) {
return false;
}
}
return true;
}
}
</syntaxhighlight>
{{ out }}
<pre>
Base 1:
The number of Fermat pseudoprimes up to 50000: 44866
The first 20: 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30 32
Base 2:
The number of Fermat pseudoprimes up to 50000: 55
The first 20: 341 561 645 1105 1387 1729 1905 2047 2465 2701 2821 3277 4033 4369 4371 4681 5461 6601 7957 8321
Base 3:
The number of Fermat pseudoprimes up to 50000: 53
The first 20: 91 121 286 671 703 949 1105 1541 1729 1891 2465 2665 2701 2821 3281 3367 3751 4961 5551 6601
Base 4:
The number of Fermat pseudoprimes up to 50000: 111
The first 20: 15 85 91 341 435 451 561 645 703 1105 1247 1271 1387 1581 1695 1729 1891 1905 2047 2071
Base 5:
The number of Fermat pseudoprimes up to 50000: 54
The first 20: 4 124 217 561 781 1541 1729 1891 2821 4123 5461 5611 5662 5731 6601 7449 7813 8029 8911 9881
Base 6:
The number of Fermat pseudoprimes up to 50000: 74
The first 20: 35 185 217 301 481 1105 1111 1261 1333 1729 2465 2701 2821 3421 3565 3589 3913 4123 4495 5713
Base 7:
The number of Fermat pseudoprimes up to 50000: 49
The first 20: 6 25 325 561 703 817 1105 1825 2101 2353 2465 3277 4525 4825 6697 8321 10225 10585 10621 11041
Base 8:
The number of Fermat pseudoprimes up to 50000: 150
The first 20: 9 21 45 63 65 105 117 133 153 231 273 341 481 511 561 585 645 651 861 949
Base 9:
The number of Fermat pseudoprimes up to 50000: 113
The first 20: 4 8 28 52 91 121 205 286 364 511 532 616 671 697 703 946 949 1036 1105 1288
Base 10:
The number of Fermat pseudoprimes up to 50000: 65
The first 20: 9 33 91 99 259 451 481 561 657 703 909 1233 1729 2409 2821 2981 3333 3367 4141 4187
Base 11:
The number of Fermat pseudoprimes up to 50000: 61
The first 20: 10 15 70 133 190 259 305 481 645 703 793 1105 1330 1729 2047 2257 2465 2821 4577 4921
Base 12:
The number of Fermat pseudoprimes up to 50000: 91
The first 20: 65 91 133 143 145 247 377 385 703 1045 1099 1105 1649 1729 1885 1891 2041 2233 2465 2701
Base 13:
The number of Fermat pseudoprimes up to 50000: 68
The first 20: 4 6 12 21 85 105 231 244 276 357 427 561 1099 1785 1891 2465 2806 3605 5028 5149
Base 14:
The number of Fermat pseudoprimes up to 50000: 69
The first 20: 15 39 65 195 481 561 781 793 841 985 1105 1111 1541 1891 2257 2465 2561 2665 2743 3277
Base 15:
The number of Fermat pseudoprimes up to 50000: 42
The first 20: 14 341 742 946 1477 1541 1687 1729 1891 1921 2821 3133 3277 4187 6541 6601 7471 8701 8911 9073
Base 16:
The number of Fermat pseudoprimes up to 50000: 145
The first 20: 15 51 85 91 255 341 435 451 561 595 645 703 1105 1247 1261 1271 1285 1387 1581 1687
Base 17:
The number of Fermat pseudoprimes up to 50000: 63
The first 20: 4 8 9 16 45 91 145 261 781 1111 1228 1305 1729 1885 2149 2821 3991 4005 4033 4187
Base 18:
The number of Fermat pseudoprimes up to 50000: 98
The first 20: 25 49 65 85 133 221 323 325 343 425 451 637 931 1105 1225 1369 1387 1649 1729 1921
Base 19:
The number of Fermat pseudoprimes up to 50000: 93
The first 20: 6 9 15 18 45 49 153 169 343 561 637 889 905 906 1035 1105 1629 1661 1849 1891
Base 20:
The number of Fermat pseudoprimes up to 50000: 66
The first 20: 21 57 133 231 399 561 671 861 889 1281 1653 1729 1891 2059 2413 2501 2761 2821 2947 3059
</pre>
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