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A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides :2''d'' − 2. For example 341 is a super-Poulet number: it has positive divisors and we have: :(211 - 2) / 11 = 2046 / 11 = 186 :(231 - 2) / 31 = 2147483646 / 31 = 69273666 :(2341 - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550 When a composite number is a pseudoprime to base 2, but not to every base (That is, not a Carmichael number), then it is a super-Poulet number, and when is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number. The super-Poulet numbers below 10,000 are : == Super-Poulet numbers with 3 or more distinct prime divisors == It is relatively easy to get super-Poulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a super-Poulet number, as you built the product of the three prime factors. Example: 2701 = 37 * 73 is a Poulet number 4033 = 37 * 109 is a Poulet number 7957 = 73 * 109 is a Poulet number so 294409 = 37 * 73 * 109 is a Poulet number too. Super-Poulet numbers with up to 7 distinct prime factors you can get with the following numbers: * * * * For example 1.118.863.200.025.063.181.061.994.266.818.401 = 6421 * 12841 * 51361 * 57781 * 115561 * 192601 * 205441 is a super-Poulet number with 7 distinct prime factors and 120 Poulet numbers. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Super-Poulet number」の詳細全文を読む スポンサード リンク
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