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Template:If prime/doc
From OeisWiki
The {{if prime}} if-then-else arithmetic function template returns {{{2|1}}} if {{{1}}} is prime (negative or positive) otherwise returns {{{3|0}}}.
The {{is prime}} predicate arithmetic function template returns 1 (if true) or 0 (if false.)
Contents
Usage
- {{if prime|input|output if true (optional, default: 1)|output if false (optional, default: 0)}}
or
- {{is prime|input}}
Valid input
Input must be an integer less than 1031 2 = 1062961.
Examples
Examples with valid input (check primes with https://oeis.org/A000040/a000040.txt N. J. A. Sloane, Table of n, prime(n) for n = 1..100000)
code result {{is prime|-5}} 1 {{is prime|-4}} 0 {{is prime|-3}} 1 {{is prime|-2}} 1 {{is prime|-1}} 0 {{is prime|0}} 0 {{is prime|1}} 0 {{is prime|2}} 1 {{is prime|3}} 1 {{is prime|4}} 0 {{is prime|5}} 1 {{if prime|6|{{yes}}|{{no}}}} 
{{if prime|6|prime|not prime}} not prime {{if prime|7|{{yes}}|{{no}}}} 
{{if prime|7|prime|not prime}} prime {{if prime|8|prime|not prime}} not prime {{if prime|9|prime|not prime}} not prime {{if prime|10|prime|not prime}} not prime {{if prime|11|prime|not prime}} prime {{if prime|12|prime|not prime}} not prime {{if prime|13|prime|not prime}} prime {{if prime|14|prime|not prime}} not prime {{if prime|15|prime|not prime}} not prime {{if prime|16|prime|not prime}} not prime {{if prime|17|prime|not prime}} prime {{if prime|19|prime|not prime}} prime {{if prime|23|prime|not prime}} prime {{if prime|29|prime|not prime}} prime {{if prime|31|prime|not prime}} prime {{if prime|37|prime|not prime}} prime {{if prime|41|prime|not prime}} prime {{if prime|199|prime|not prime}} prime {{if prime|257|prime|not prime}} prime {{if prime|999|prime|not prime}} not prime {{if prime|1001|prime|not prime}} not prime {{if prime|10001|prime|not prime}} not prime {{if prime|10003|prime|not prime}} not prime {{if prime|10005|prime|not prime}} not prime {{if prime|10007|prime|not prime}} prime {{if prime|10009|prime|not prime}} prime {{if prime|17160|prime|not prime}} not prime {{if prime|65536|prime|not prime}} not prime {{if prime|65537|prime|not prime}} prime {{if prime|65539|prime|not prime}} prime {{if prime|65541|prime|not prime}} not prime {{if prime|65543|prime|not prime}} prime {{if prime|65545|prime|not prime}} not prime {{if prime|65547|prime|not prime}} not prime {{if prime|65549|prime|not prime}} not prime {{if prime|65551|prime|not prime}} prime {{if prime|65553|prime|not prime}} not prime {{if prime|65555|prime|not prime}} not prime {{if prime|65557|prime|not prime}} prime {{if prime|65559|prime|not prime}} not prime {{if prime|65561|prime|not prime}} not prime {{if prime|65563|prime|not prime}} prime {{if prime|65567|prime|not prime}} not prime {{if prime|65569|prime|not prime}} not prime {{if prime|65571|prime|not prime}} not prime {{if prime|65573|prime|not prime}} not prime {{if prime|65577|prime|not prime}} not prime {{if prime|65579|prime|not prime}} prime {{if prime|65581|prime|not prime}} prime {{if prime|65583|prime|not prime}} not prime {{if prime|65587|prime|not prime}} prime {{if prime|65589|prime|not prime}} not prime {{if prime|65591|prime|not prime}} not prime {{if prime|65593|prime|not prime}} not prime {{if prime|65597|prime|not prime}} not prime {{if prime|65599|prime|not prime}} prime {{if prime|965536|prime|not prime}} not prime {{if prime|965537|prime|not prime}} not prime {{if prime|965539|prime|not prime}} not prime {{if prime|965541|prime|not prime}} not prime {{if prime|965543|prime|not prime}} not prime {{if prime|965545|prime|not prime}} not prime {{if prime|965547|prime|not prime}} not prime {{if prime|965549|prime|not prime}} not prime {{if prime|965551|prime|not prime}} prime {{if prime|965553|prime|not prime}} not prime {{if prime|965555|prime|not prime}} not prime {{if prime|965557|prime|not prime}} not prime {{if prime|965559|prime|not prime}} not prime {{if prime|965561|prime|not prime}} not prime {{if prime|965563|prime|not prime}} not prime {{if prime|965567|prime|not prime}} prime {{if prime|965569|prime|not prime}} not prime {{if prime|965571|prime|not prime}} not prime {{if prime|965573|prime|not prime}} not prime {{if prime|965577|prime|not prime}} not prime {{if prime|965579|prime|not prime}} not prime {{if prime|965581|prime|not prime}} not prime {{if prime|965583|prime|not prime}} not prime {{if prime|965587|prime|not prime}} not prime {{if prime|965589|prime|not prime}} not prime {{if prime|965591|prime|not prime}} not prime {{if prime|965593|prime|not prime}} not prime {{if prime|965597|prime|not prime}} not prime {{if prime|965599|prime|not prime}} not prime {{if prime|965601|prime|not prime}} not prime {{if prime|965603|prime|not prime}} prime {{if prime|965607|prime|not prime}} not prime {{if prime|965609|prime|not prime}} not prime {{if prime|965611|prime|not prime}} prime {{if prime|965613|prime|not prime}} not prime {{if prime|965617|prime|not prime}} not prime {{if prime|965619|prime|not prime}} not prime {{if prime|965621|prime|not prime}} prime {{if prime|965623|prime|not prime}} prime {{if prime|1021^2|prime|not prime}} not prime {{if prime|1031^2 - 1|prime|not prime}} not prime {{if prime|+1000|prime|not prime}} not prime {{if prime|10.0|prime|not prime}} not prime {{if prime|floor pi|prime|not prime}} prime {{if prime|floor (pi^2)|prime|not prime}} not prime {{if prime|{{Fibonacci|10}}|prime|not prime}} not prime {{if prime|{{Fibonacci|11}}|prime|not prime}} prime
Examples with invalid input
code result {{if prime|1031^2|prime|not prime}} If prime error: Argument must be an integer with absolute value less than 1031 2 = 1062961 {{if prime}} If prime error: Argument must be an integer {{if prime|one}} If prime error: Argument must be an integer {{if prime|-0.1}} If prime error: Argument must be an integer {{if prime|0.897}} If prime error: Argument must be an integer {{if prime|1.523}} If prime error: Argument must be an integer {{if prime|-34.2}} If prime error: Argument must be an integer {{if prime|pi}} If prime error: Argument must be an integer
Formatted numbers
This template requires unformatted numbers, it will not recognize formatted numbers, e.g. comma separated, which is by design since formatted numbers will break expression parsers. To remove the formatting from a number, you can wrap the number first in {{formatnum:number|R}}.[1]
code result {{if prime|1,000|prime|not prime}} If prime error: Argument must be an integer {{if prime|{{formatnum:1,000|R}}|prime|not prime}} not prime
Code
A000040: The prime numbers. https://oeis.org/A000040/a000040.txt {{list | create | from = b-file | input = 1 2 2 3 3 5 4 7 5 11 6 13 7 17 8 19 9 23 10 29 11 31 12 37 13 41 14 43 15 47 16 53 17 59 18 61 19 67 20 71 21 73 22 79 23 83 24 89 25 97 26 101 27 103 28 107 29 109 30 113 31 127 32 131 33 137 34 139 35 149 36 151 37 157 38 163 39 167 40 173 41 179 42 181 43 191 44 193 45 197 46 199 47 211 48 223 49 227 50 229 51 233 52 239 53 241 54 251 55 257 56 263 57 269 58 271 59 277 60 281 61 283 62 293 63 307 64 311 65 313 66 317 67 331 68 337 69 347 70 349 71 353 72 359 73 367 74 373 75 379 76 383 77 389 78 397 79 401 80 409 81 419 82 421 83 431 84 433 85 439 86 443 87 449 88 457 89 461 90 463 91 467 92 479 93 487 94 491 95 499 96 503 97 509 98 521 99 523 100 541 101 547 102 557 103 563 104 569 105 571 106 577 107 587 108 593 109 599 110 601 111 607 112 613 113 617 114 619 115 631 116 641 117 643 118 647 119 653 120 659 121 661 122 673 123 677 124 683 125 691 126 701 127 709 128 719 129 727 130 733 131 739 132 743 133 751 134 757 135 761 136 769 137 773 138 787 139 797 140 809 141 811 142 821 143 823 144 827 145 829 146 839 147 853 148 857 149 859 150 863 151 877 152 881 153 883 154 887 155 907 156 911 157 919 158 929 159 937 160 941 161 947 162 953 163 967 164 971 165 977 166 983 167 991 168 997 169 1009 170 1013 171 1019 172 1021 173 1031 }} gives 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031
<noinclude>{{documentation}}<!--
A000040 The prime numbers.
The 172 primes less than 2^10 = 1024 are:
n a(n)
1 2
2 3
3 5
4 7
5 11
6 13
7 17
8 19
9 23
(...)
165 977
166 983
167 991
168 997
169 1009
170 1013
171 1019
172 1021
The next prime is:
173 1031
--></noinclude><includeonly>{{ifint| {{{1|NAN}}}
| {{#ifexpr: ( abs ({{{1}}}) ) < 1031^2
| {{#ifexpr: ( abs ({{{1}}}) ) > 1
| {{#ifexpr: (
<!--
A000040 The prime numbers.
The 172 primes less than 2^10 = 1024 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021
-->
<!-- 1 -->{{#ifexpr: ( 2 * 2) <= abs ({{{1}}}) | abs ({{{1}}}) mod 2 | 1 }} and
<!-- 2 -->{{#ifexpr: ( 3 * 3) <= abs ({{{1}}}) | abs ({{{1}}}) mod 3 | 1 }} and
<!-- 3 -->{{#ifexpr: ( 5 * 5) <= abs ({{{1}}}) | abs ({{{1}}}) mod 5 | 1 }} and
<!-- 4 -->{{#ifexpr: ( 7 * 7) <= abs ({{{1}}}) | abs ({{{1}}}) mod 7 | 1 }} and
<!-- 5 -->{{#ifexpr: ( 11 * 11) <= abs ({{{1}}}) | abs ({{{1}}}) mod 11 | 1 }} and
<!-- 6 -->{{#ifexpr: ( 13 * 13) <= abs ({{{1}}}) | abs ({{{1}}}) mod 13 | 1 }} and
<!-- 7 -->{{#ifexpr: ( 17 * 17) <= abs ({{{1}}}) | abs ({{{1}}}) mod 17 | 1 }} and
<!-- 8 -->{{#ifexpr: ( 19 * 19) <= abs ({{{1}}}) | abs ({{{1}}}) mod 19 | 1 }} and
<!-- 9 -->{{#ifexpr: ( 23 * 23) <= abs ({{{1}}}) | abs ({{{1}}}) mod 23 | 1 }} and
<!-- 10 -->{{#ifexpr: ( 29 * 29) <= abs ({{{1}}}) | abs ({{{1}}}) mod 29 | 1 }} and
<!-- 11 -->{{#ifexpr: ( 31 * 31) <= abs ({{{1}}}) | abs ({{{1}}}) mod 31 | 1 }} and
<!-- 12 -->{{#ifexpr: ( 37 * 37) <= abs ({{{1}}}) | abs ({{{1}}}) mod 37 | 1 }} and
<!-- 13 -->{{#ifexpr: ( 41 * 41) <= abs ({{{1}}}) | abs ({{{1}}}) mod 41 | 1 }} and
<!-- 14 -->{{#ifexpr: ( 43 * 43) <= abs ({{{1}}}) | abs ({{{1}}}) mod 43 | 1 }} and
<!-- 15 -->{{#ifexpr: ( 47 * 47) <= abs ({{{1}}}) | abs ({{{1}}}) mod 47 | 1 }} and
<!-- 16 -->{{#ifexpr: ( 53 * 53) <= abs ({{{1}}}) | abs ({{{1}}}) mod 53 | 1 }} and
<!-- 17 -->{{#ifexpr: ( 59 * 59) <= abs ({{{1}}}) | abs ({{{1}}}) mod 59 | 1 }} and
<!-- 18 -->{{#ifexpr: ( 61 * 61) <= abs ({{{1}}}) | abs ({{{1}}}) mod 61 | 1 }} and
<!-- 19 -->{{#ifexpr: ( 67 * 67) <= abs ({{{1}}}) | abs ({{{1}}}) mod 67 | 1 }} and
<!-- 20 -->{{#ifexpr: ( 71 * 71) <= abs ({{{1}}}) | abs ({{{1}}}) mod 71 | 1 }} and
<!-- 21 -->{{#ifexpr: ( 73 * 73) <= abs ({{{1}}}) | abs ({{{1}}}) mod 73 | 1 }} and
<!-- 22 -->{{#ifexpr: ( 79 * 79) <= abs ({{{1}}}) | abs ({{{1}}}) mod 79 | 1 }} and
<!-- 23 -->{{#ifexpr: ( 83 * 83) <= abs ({{{1}}}) | abs ({{{1}}}) mod 83 | 1 }} and
<!-- 24 -->{{#ifexpr: ( 89 * 89) <= abs ({{{1}}}) | abs ({{{1}}}) mod 89 | 1 }} and
<!-- 25 -->{{#ifexpr: ( 97 * 97) <= abs ({{{1}}}) | abs ({{{1}}}) mod 97 | 1 }} and
<!-- 26 -->{{#ifexpr: (101 * 101) <= abs ({{{1}}}) | abs ({{{1}}}) mod 101 | 1 }} and
<!-- 27 -->{{#ifexpr: (103 * 103) <= abs ({{{1}}}) | abs ({{{1}}}) mod 103 | 1 }} and
<!-- 28 -->{{#ifexpr: (107 * 107) <= abs ({{{1}}}) | abs ({{{1}}}) mod 107 | 1 }} and
<!-- 29 -->{{#ifexpr: (109 * 109) <= abs ({{{1}}}) | abs ({{{1}}}) mod 109 | 1 }} and
<!-- 30 -->{{#ifexpr: (113 * 113) <= abs ({{{1}}}) | abs ({{{1}}}) mod 113 | 1 }} and
<!-- 31 -->{{#ifexpr: (127 * 127) <= abs ({{{1}}}) | abs ({{{1}}}) mod 127 | 1 }}
{{#ifexpr: (131 * 131) <= abs ({{{1}}}) | and
<!-- 32 -->{{#ifexpr: (131 * 131) <= abs ({{{1}}}) | abs ({{{1}}}) mod 131 | 1 }} and
<!-- 33 -->{{#ifexpr: (137 * 137) <= abs ({{{1}}}) | abs ({{{1}}}) mod 137 | 1 }} and
<!-- 34 -->{{#ifexpr: (139 * 139) <= abs ({{{1}}}) | abs ({{{1}}}) mod 139 | 1 }} and
<!-- 35 -->{{#ifexpr: (149 * 149) <= abs ({{{1}}}) | abs ({{{1}}}) mod 149 | 1 }} and
<!-- 36 -->{{#ifexpr: (151 * 151) <= abs ({{{1}}}) | abs ({{{1}}}) mod 151 | 1 }} and
<!-- 37 -->{{#ifexpr: (157 * 157) <= abs ({{{1}}}) | abs ({{{1}}}) mod 157 | 1 }} and
<!-- 38 -->{{#ifexpr: (163 * 163) <= abs ({{{1}}}) | abs ({{{1}}}) mod 163 | 1 }} and
<!-- 39 -->{{#ifexpr: (167 * 167) <= abs ({{{1}}}) | abs ({{{1}}}) mod 167 | 1 }} and
<!-- 40 -->{{#ifexpr: (173 * 173) <= abs ({{{1}}}) | abs ({{{1}}}) mod 173 | 1 }} and
<!-- 41 -->{{#ifexpr: (179 * 179) <= abs ({{{1}}}) | abs ({{{1}}}) mod 179 | 1 }} and
<!-- 42 -->{{#ifexpr: (181 * 181) <= abs ({{{1}}}) | abs ({{{1}}}) mod 181 | 1 }} and
<!-- 43 -->{{#ifexpr: (191 * 191) <= abs ({{{1}}}) | abs ({{{1}}}) mod 191 | 1 }} and
<!-- 44 -->{{#ifexpr: (193 * 193) <= abs ({{{1}}}) | abs ({{{1}}}) mod 193 | 1 }} and
<!-- 45 -->{{#ifexpr: (197 * 197) <= abs ({{{1}}}) | abs ({{{1}}}) mod 197 | 1 }} and
<!-- 46 -->{{#ifexpr: (199 * 199) <= abs ({{{1}}}) | abs ({{{1}}}) mod 199 | 1 }} and
<!-- 47 -->{{#ifexpr: (211 * 211) <= abs ({{{1}}}) | abs ({{{1}}}) mod 211 | 1 }} and
<!-- 48 -->{{#ifexpr: (223 * 223) <= abs ({{{1}}}) | abs ({{{1}}}) mod 223 | 1 }} and
<!-- 49 -->{{#ifexpr: (227 * 227) <= abs ({{{1}}}) | abs ({{{1}}}) mod 227 | 1 }} and
<!-- 50 -->{{#ifexpr: (229 * 229) <= abs ({{{1}}}) | abs ({{{1}}}) mod 229 | 1 }} and
<!-- 51 -->{{#ifexpr: (233 * 233) <= abs ({{{1}}}) | abs ({{{1}}}) mod 233 | 1 }} and
<!-- 52 -->{{#ifexpr: (239 * 239) <= abs ({{{1}}}) | abs ({{{1}}}) mod 239 | 1 }} and
<!-- 53 -->{{#ifexpr: (241 * 241) <= abs ({{{1}}}) | abs ({{{1}}}) mod 241 | 1 }} and
<!-- 54 -->{{#ifexpr: (251 * 251) <= abs ({{{1}}}) | abs ({{{1}}}) mod 251 | 1 }}
}}
<!--
A000040 The prime numbers.
The 172 primes less than 2^10 = 1024 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021
-->
{{#ifexpr: (257 * 257) <= abs ({{{1}}}) | and
<!-- 55 -->{{#ifexpr: (257 * 257) <= abs ({{{1}}}) | abs ({{{1}}}) mod 257 | 1 }} and
<!-- 56 -->{{#ifexpr: (263 * 263) <= abs ({{{1}}}) | abs ({{{1}}}) mod 263 | 1 }} and
<!-- 57 -->{{#ifexpr: (269 * 269) <= abs ({{{1}}}) | abs ({{{1}}}) mod 269 | 1 }} and
<!-- 58 -->{{#ifexpr: (271 * 271) <= abs ({{{1}}}) | abs ({{{1}}}) mod 271 | 1 }} and
<!-- 59 -->{{#ifexpr: (277 * 277) <= abs ({{{1}}}) | abs ({{{1}}}) mod 277 | 1 }} and
<!-- 60 -->{{#ifexpr: (281 * 281) <= abs ({{{1}}}) | abs ({{{1}}}) mod 281 | 1 }} and
<!-- 61 -->{{#ifexpr: (283 * 283) <= abs ({{{1}}}) | abs ({{{1}}}) mod 283 | 1 }} and
<!-- 62 -->{{#ifexpr: (293 * 293) <= abs ({{{1}}}) | abs ({{{1}}}) mod 293 | 1 }} and
<!-- 63 -->{{#ifexpr: (307 * 307) <= abs ({{{1}}}) | abs ({{{1}}}) mod 307 | 1 }} and
<!-- 64 -->{{#ifexpr: (311 * 311) <= abs ({{{1}}}) | abs ({{{1}}}) mod 311 | 1 }} and
<!-- 65 -->{{#ifexpr: (313 * 313) <= abs ({{{1}}}) | abs ({{{1}}}) mod 313 | 1 }} and
<!-- 66 -->{{#ifexpr: (317 * 317) <= abs ({{{1}}}) | abs ({{{1}}}) mod 317 | 1 }} and
<!-- 67 -->{{#ifexpr: (331 * 331) <= abs ({{{1}}}) | abs ({{{1}}}) mod 331 | 1 }} and
<!-- 68 -->{{#ifexpr: (337 * 337) <= abs ({{{1}}}) | abs ({{{1}}}) mod 337 | 1 }} and
<!-- 69 -->{{#ifexpr: (347 * 347) <= abs ({{{1}}}) | abs ({{{1}}}) mod 347 | 1 }} and
<!-- 70 -->{{#ifexpr: (349 * 349) <= abs ({{{1}}}) | abs ({{{1}}}) mod 349 | 1 }} and
<!-- 71 -->{{#ifexpr: (353 * 353) <= abs ({{{1}}}) | abs ({{{1}}}) mod 353 | 1 }} and
<!-- 72 -->{{#ifexpr: (359 * 359) <= abs ({{{1}}}) | abs ({{{1}}}) mod 359 | 1 }} and
<!-- 73 -->{{#ifexpr: (367 * 367) <= abs ({{{1}}}) | abs ({{{1}}}) mod 367 | 1 }} and
<!-- 74 -->{{#ifexpr: (373 * 373) <= abs ({{{1}}}) | abs ({{{1}}}) mod 373 | 1 }} and
<!-- 75 -->{{#ifexpr: (379 * 379) <= abs ({{{1}}}) | abs ({{{1}}}) mod 379 | 1 }} and
<!-- 76 -->{{#ifexpr: (383 * 383) <= abs ({{{1}}}) | abs ({{{1}}}) mod 383 | 1 }} and
<!-- 77 -->{{#ifexpr: (389 * 389) <= abs ({{{1}}}) | abs ({{{1}}}) mod 389 | 1 }} and
<!-- 78 -->{{#ifexpr: (397 * 397) <= abs ({{{1}}}) | abs ({{{1}}}) mod 397 | 1 }} and
<!-- 79 -->{{#ifexpr: (401 * 401) <= abs ({{{1}}}) | abs ({{{1}}}) mod 401 | 1 }} and
<!-- 80 -->{{#ifexpr: (409 * 409) <= abs ({{{1}}}) | abs ({{{1}}}) mod 409 | 1 }} and
<!-- 81 -->{{#ifexpr: (419 * 419) <= abs ({{{1}}}) | abs ({{{1}}}) mod 419 | 1 }} and
<!-- 82 -->{{#ifexpr: (421 * 421) <= abs ({{{1}}}) | abs ({{{1}}}) mod 421 | 1 }} and
<!-- 83 -->{{#ifexpr: (431 * 431) <= abs ({{{1}}}) | abs ({{{1}}}) mod 431 | 1 }} and
<!-- 84 -->{{#ifexpr: (433 * 433) <= abs ({{{1}}}) | abs ({{{1}}}) mod 433 | 1 }} and
<!-- 85 -->{{#ifexpr: (439 * 439) <= abs ({{{1}}}) | abs ({{{1}}}) mod 439 | 1 }} and
<!-- 86 -->{{#ifexpr: (443 * 443) <= abs ({{{1}}}) | abs ({{{1}}}) mod 443 | 1 }} and
<!-- 87 -->{{#ifexpr: (449 * 449) <= abs ({{{1}}}) | abs ({{{1}}}) mod 449 | 1 }} and
<!-- 88 -->{{#ifexpr: (457 * 457) <= abs ({{{1}}}) | abs ({{{1}}}) mod 457 | 1 }} and
<!-- 89 -->{{#ifexpr: (461 * 461) <= abs ({{{1}}}) | abs ({{{1}}}) mod 461 | 1 }} and
<!-- 90 -->{{#ifexpr: (463 * 463) <= abs ({{{1}}}) | abs ({{{1}}}) mod 463 | 1 }} and
<!-- 91 -->{{#ifexpr: (467 * 467) <= abs ({{{1}}}) | abs ({{{1}}}) mod 467 | 1 }} and
<!-- 92 -->{{#ifexpr: (479 * 479) <= abs ({{{1}}}) | abs ({{{1}}}) mod 479 | 1 }} and
<!-- 93 -->{{#ifexpr: (487 * 487) <= abs ({{{1}}}) | abs ({{{1}}}) mod 487 | 1 }} and
<!-- 94 -->{{#ifexpr: (491 * 491) <= abs ({{{1}}}) | abs ({{{1}}}) mod 491 | 1 }} and
<!-- 95 -->{{#ifexpr: (499 * 499) <= abs ({{{1}}}) | abs ({{{1}}}) mod 499 | 1 }} and
<!-- 96 -->{{#ifexpr: (503 * 503) <= abs ({{{1}}}) | abs ({{{1}}}) mod 503 | 1 }} and
<!-- 97 -->{{#ifexpr: (509 * 509) <= abs ({{{1}}}) | abs ({{{1}}}) mod 509 | 1 }}
}}
<!--
A000040 The prime numbers.
The 172 primes less than 2^10 = 1024 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021
-->
{{#ifexpr: (521 * 521) <= abs ({{{1}}}) | and
<!-- 98 -->{{#ifexpr: (521 * 521) <= abs ({{{1}}}) | abs ({{{1}}}) mod 521 | 1 }} and
<!-- 99 -->{{#ifexpr: (523 * 523) <= abs ({{{1}}}) | abs ({{{1}}}) mod 523 | 1 }} and
<!-- 100 -->{{#ifexpr: (541 * 541) <= abs ({{{1}}}) | abs ({{{1}}}) mod 541 | 1 }} and
<!-- 101 -->{{#ifexpr: (547 * 547) <= abs ({{{1}}}) | abs ({{{1}}}) mod 547 | 1 }} and
<!-- 102 -->{{#ifexpr: (557 * 557) <= abs ({{{1}}}) | abs ({{{1}}}) mod 557 | 1 }} and
<!-- 103 -->{{#ifexpr: (563 * 563) <= abs ({{{1}}}) | abs ({{{1}}}) mod 563 | 1 }} and
<!-- 104 -->{{#ifexpr: (569 * 569) <= abs ({{{1}}}) | abs ({{{1}}}) mod 569 | 1 }} and
<!-- 105 -->{{#ifexpr: (571 * 571) <= abs ({{{1}}}) | abs ({{{1}}}) mod 571 | 1 }} and
<!-- 106 -->{{#ifexpr: (577 * 577) <= abs ({{{1}}}) | abs ({{{1}}}) mod 577 | 1 }} and
<!-- 107 -->{{#ifexpr: (587 * 587) <= abs ({{{1}}}) | abs ({{{1}}}) mod 587 | 1 }} and
<!-- 108 -->{{#ifexpr: (593 * 593) <= abs ({{{1}}}) | abs ({{{1}}}) mod 593 | 1 }} and
<!-- 109 -->{{#ifexpr: (599 * 599) <= abs ({{{1}}}) | abs ({{{1}}}) mod 599 | 1 }} and
<!-- 110 -->{{#ifexpr: (601 * 601) <= abs ({{{1}}}) | abs ({{{1}}}) mod 601 | 1 }} and
<!-- 111 -->{{#ifexpr: (607 * 607) <= abs ({{{1}}}) | abs ({{{1}}}) mod 607 | 1 }} and
<!-- 112 -->{{#ifexpr: (613 * 613) <= abs ({{{1}}}) | abs ({{{1}}}) mod 613 | 1 }} and
<!-- 113 -->{{#ifexpr: (617 * 617) <= abs ({{{1}}}) | abs ({{{1}}}) mod 617 | 1 }} and
<!-- 114 -->{{#ifexpr: (619 * 619) <= abs ({{{1}}}) | abs ({{{1}}}) mod 619 | 1 }} and
<!-- 115 -->{{#ifexpr: (631 * 631) <= abs ({{{1}}}) | abs ({{{1}}}) mod 631 | 1 }} and
<!-- 116 -->{{#ifexpr: (641 * 641) <= abs ({{{1}}}) | abs ({{{1}}}) mod 641 | 1 }} and
<!-- 117 -->{{#ifexpr: (643 * 643) <= abs ({{{1}}}) | abs ({{{1}}}) mod 643 | 1 }} and
<!-- 118 -->{{#ifexpr: (647 * 647) <= abs ({{{1}}}) | abs ({{{1}}}) mod 647 | 1 }} and
<!-- 119 -->{{#ifexpr: (653 * 653) <= abs ({{{1}}}) | abs ({{{1}}}) mod 653 | 1 }} and
<!-- 120 -->{{#ifexpr: (659 * 659) <= abs ({{{1}}}) | abs ({{{1}}}) mod 659 | 1 }} and
<!-- 121 -->{{#ifexpr: (661 * 661) <= abs ({{{1}}}) | abs ({{{1}}}) mod 661 | 1 }} and
<!-- 122 -->{{#ifexpr: (673 * 673) <= abs ({{{1}}}) | abs ({{{1}}}) mod 673 | 1 }} and
<!-- 123 -->{{#ifexpr: (677 * 677) <= abs ({{{1}}}) | abs ({{{1}}}) mod 677 | 1 }} and
<!-- 124 -->{{#ifexpr: (683 * 683) <= abs ({{{1}}}) | abs ({{{1}}}) mod 683 | 1 }} and
<!-- 125 -->{{#ifexpr: (691 * 691) <= abs ({{{1}}}) | abs ({{{1}}}) mod 691 | 1 }} and
<!-- 126 -->{{#ifexpr: (701 * 701) <= abs ({{{1}}}) | abs ({{{1}}}) mod 701 | 1 }} and
<!-- 127 -->{{#ifexpr: (709 * 709) <= abs ({{{1}}}) | abs ({{{1}}}) mod 709 | 1 }} and
<!-- 128 -->{{#ifexpr: (719 * 719) <= abs ({{{1}}}) | abs ({{{1}}}) mod 719 | 1 }} and
<!-- 129 -->{{#ifexpr: (727 * 727) <= abs ({{{1}}}) | abs ({{{1}}}) mod 727 | 1 }} and
<!-- 130 -->{{#ifexpr: (733 * 733) <= abs ({{{1}}}) | abs ({{{1}}}) mod 733 | 1 }} and
<!-- 131 -->{{#ifexpr: (739 * 739) <= abs ({{{1}}}) | abs ({{{1}}}) mod 739 | 1 }} and
<!-- 132 -->{{#ifexpr: (743 * 743) <= abs ({{{1}}}) | abs ({{{1}}}) mod 743 | 1 }} and
<!-- 133 -->{{#ifexpr: (751 * 751) <= abs ({{{1}}}) | abs ({{{1}}}) mod 751 | 1 }} and
<!-- 134 -->{{#ifexpr: (757 * 757) <= abs ({{{1}}}) | abs ({{{1}}}) mod 757 | 1 }} and
<!-- 135 -->{{#ifexpr: (761 * 761) <= abs ({{{1}}}) | abs ({{{1}}}) mod 761 | 1 }}
}}
<!--
A000040 The prime numbers.
The 172 primes less than 2^10 = 1024 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021
-->
{{#ifexpr: (769 * 769) <= abs ({{{1}}}) | and
<!-- 136 -->{{#ifexpr: (769 * 769) <= abs ({{{1}}}) | abs ({{{1}}}) mod 769 | 1 }} and
<!-- 137 -->{{#ifexpr: (773 * 773) <= abs ({{{1}}}) | abs ({{{1}}}) mod 773 | 1 }} and
<!-- 138 -->{{#ifexpr: (787 * 787) <= abs ({{{1}}}) | abs ({{{1}}}) mod 787 | 1 }} and
<!-- 139 -->{{#ifexpr: (797 * 797) <= abs ({{{1}}}) | abs ({{{1}}}) mod 797 | 1 }} and
<!-- 140 -->{{#ifexpr: (809 * 809) <= abs ({{{1}}}) | abs ({{{1}}}) mod 809 | 1 }} and
<!-- 141 -->{{#ifexpr: (811 * 811) <= abs ({{{1}}}) | abs ({{{1}}}) mod 811 | 1 }} and
<!-- 142 -->{{#ifexpr: (821 * 821) <= abs ({{{1}}}) | abs ({{{1}}}) mod 821 | 1 }} and
<!-- 143 -->{{#ifexpr: (823 * 823) <= abs ({{{1}}}) | abs ({{{1}}}) mod 823 | 1 }} and
<!-- 144 -->{{#ifexpr: (827 * 827) <= abs ({{{1}}}) | abs ({{{1}}}) mod 827 | 1 }} and
<!-- 145 -->{{#ifexpr: (829 * 829) <= abs ({{{1}}}) | abs ({{{1}}}) mod 829 | 1 }} and
<!-- 146 -->{{#ifexpr: (839 * 839) <= abs ({{{1}}}) | abs ({{{1}}}) mod 839 | 1 }} and
<!-- 147 -->{{#ifexpr: (853 * 853) <= abs ({{{1}}}) | abs ({{{1}}}) mod 853 | 1 }} and
<!-- 148 -->{{#ifexpr: (857 * 857) <= abs ({{{1}}}) | abs ({{{1}}}) mod 857 | 1 }} and
<!-- 149 -->{{#ifexpr: (859 * 859) <= abs ({{{1}}}) | abs ({{{1}}}) mod 859 | 1 }} and
<!-- 150 -->{{#ifexpr: (863 * 863) <= abs ({{{1}}}) | abs ({{{1}}}) mod 863 | 1 }} and
<!-- 151 -->{{#ifexpr: (877 * 877) <= abs ({{{1}}}) | abs ({{{1}}}) mod 877 | 1 }} and
<!-- 152 -->{{#ifexpr: (881 * 881) <= abs ({{{1}}}) | abs ({{{1}}}) mod 881 | 1 }} and
<!-- 153 -->{{#ifexpr: (883 * 883) <= abs ({{{1}}}) | abs ({{{1}}}) mod 883 | 1 }} and
<!-- 154 -->{{#ifexpr: (887 * 887) <= abs ({{{1}}}) | abs ({{{1}}}) mod 887 | 1 }} and
<!-- 155 -->{{#ifexpr: (907 * 907) <= abs ({{{1}}}) | abs ({{{1}}}) mod 907 | 1 }} and
<!-- 156 -->{{#ifexpr: (911 * 911) <= abs ({{{1}}}) | abs ({{{1}}}) mod 911 | 1 }} and
<!-- 157 -->{{#ifexpr: (919 * 919) <= abs ({{{1}}}) | abs ({{{1}}}) mod 919 | 1 }} and
<!-- 158 -->{{#ifexpr: (929 * 929) <= abs ({{{1}}}) | abs ({{{1}}}) mod 929 | 1 }} and
<!-- 159 -->{{#ifexpr: (937 * 937) <= abs ({{{1}}}) | abs ({{{1}}}) mod 937 | 1 }} and
<!-- 160 -->{{#ifexpr: (941 * 941) <= abs ({{{1}}}) | abs ({{{1}}}) mod 941 | 1 }} and
<!-- 161 -->{{#ifexpr: (947 * 947) <= abs ({{{1}}}) | abs ({{{1}}}) mod 947 | 1 }} and
<!-- 162 -->{{#ifexpr: (953 * 953) <= abs ({{{1}}}) | abs ({{{1}}}) mod 953 | 1 }} and
<!-- 163 -->{{#ifexpr: (967 * 967) <= abs ({{{1}}}) | abs ({{{1}}}) mod 967 | 1 }} and
<!-- 164 -->{{#ifexpr: (971 * 971) <= abs ({{{1}}}) | abs ({{{1}}}) mod 971 | 1 }} and
<!-- 165 -->{{#ifexpr: (977 * 977) <= abs ({{{1}}}) | abs ({{{1}}}) mod 977 | 1 }} and
<!-- 166 -->{{#ifexpr: (983 * 983) <= abs ({{{1}}}) | abs ({{{1}}}) mod 983 | 1 }} and
<!-- 167 -->{{#ifexpr: (991 * 991) <= abs ({{{1}}}) | abs ({{{1}}}) mod 991 | 1 }} and
<!-- 168 -->{{#ifexpr: (997 * 997) <= abs ({{{1}}}) | abs ({{{1}}}) mod 997 | 1 }} and
<!-- 169 -->{{#ifexpr: (1009 * 1009) <= abs ({{{1}}}) | abs ({{{1}}}) mod 1009 | 1 }} and
<!-- 170 -->{{#ifexpr: (1013 * 1013) <= abs ({{{1}}}) | abs ({{{1}}}) mod 1013 | 1 }} and
<!-- 171 -->{{#ifexpr: (1019 * 1019) <= abs ({{{1}}}) | abs ({{{1}}}) mod 1019 | 1 }} and
<!-- 172 -->{{#ifexpr: (1021 * 1021) <= abs ({{{1}}}) | abs ({{{1}}}) mod 1021 | 1 }}
<!--
The code now allows to check the primality of any number < 1031^2 (and in particular of any number < 2^20.)
Going any further with this primitive method is just too impractical using Mediawiki templates.
-->
}}
) = 1
| {{{2|1}}}
| {{{3|0}}}
}}
| {{{3|0}}}
}}
| {{error| If prime error: Argument must be an integer with absolute value less than 1031{{^|2}} {{=}} {{#expr: 1031^2}} }}
}}
| {{error| If prime error: Argument must be an integer }}
}}</includeonly>
See also
- {{distinct prime factors up to sqrt(n)}} or {{dpf le sqrt(n)}}
- {{distinct nontrivial prime factors}} or {{dpf lt n}}
- {{distinct prime factors}} or {{dpf}}
- {{number of distinct prime factors}} or {{little omega}}
- {{sum of distinct prime factors}} or {{sodpf}}
- {{product of distinct prime factors}} or {{squarefree kernel}} or {{radical}} or {{rad}}
- {{multiplicity}}
- {{prime factors (with multiplicity) up to sqrt(n)}} or {{mpf le sqrt(n)}}
- {{nontrivial prime factors (with multiplicity)}} or {{mpf lt n}}
- {{prime factors (with multiplicity)}} or {{mpf}} or {{factorization}}
- {{number of prime factors (with multiplicity)}} or {{big Omega}}
- {{sum of prime factors (with multiplicity)}} or {{sopfr}} or {{integer log}}
- {{product of prime factors (with multiplicity)}} (must give back {{abs|n}}, the absolute value of
)n
- {{quadratfrei}}
- {{Moebius mu}} or {{mu}}
- {{Euler phi}} or {{totient}}
- {{Dedekind psi}}
- {{number of divisors}} or {{sigma 0}} or {{tau}}
- {{sum of divisors}} or {{sigma 1}} or {{sigma}} (Cf. {{divisor function}} or {{sigma k}}, with
(default value))k = 1 - {{divisor function}} or {{sigma k}} (for
)k ≠ 0
External links
- Andrew Hodges, Java Applet for Factorization
- http://factordb.com/
