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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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The smallest base-2 pseudoprime q such that 2q+1 is also a base-2 pseudoprime — a “Sophie Germain pseudoprime,” so to speak. Using Feitsma’s table, one can find two more such numbers < 2^64: 23456248059221 = R23 and 96076792050570581 = R29, where Rn = (4^n-1)/3 is a repunit in radix 4, which often yields a large Sophie Germain pseudoprime; 9890881 (a Carmichael number) is not of the same type. Can we find a “pseudo-Cunningham chain” of length 3? [Yosei]

 

  Submitted: 2019-07-22 08:13:27;   Last Modified: 2019-07-22 09:05:27.



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