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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest base2 pseudoprime q such that 2q+1 is also a base2 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^n1)/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 “pseudoCunningham chain” of length 3? [Yosei]
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