Super-Poulet number
A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d divides 2ᵈ − 2. For example, 341 is a super-Poulet number: it has positive divisors {1, 11, 31, 341} and we have: (2¹¹ - 2) / 11 = 2046 / 11 = 186 (2³¹ - 2) / 31 = 2147483646 / 31 = 69273666 (2³⁴¹ - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550 When is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number.

Super-Poulet number

Section Title:
Table Section Text: A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d divides 2ᵈ − 2. For example, 341 is a super-Poulet number: it has positive divisors {1, 11, 31, 341} and we have: (2¹¹ - 2) / 11 = 2046 / 11 = 186 (2³¹ - 2) / 31 = 2147483646 / 31 = 69273666 (2³⁴¹ - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550 When is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number.

n

1	341 = 11 × 31

2	1387 = 19 × 73

3	2047 = 23 × 89

4	2701 = 37 × 73

5	3277 = 29 × 113

6	4033 = 37 × 109

7	4369 = 17 × 257

8	4681 = 31 × 151

9	5461 = 43 × 127

10	7957 = 73 × 109

11	8321 = 53 × 157

Sentence(s)

2701 = 37 * 73, 4033 = 37 * 109, 7957 = 73 * 109 are Poulet numbers.

final_sentence: 2701 = 37 * 73, 4033 = 37 * 109, 7957 = 73 * 109 are Poulet numbers.