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

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Kari Phillips ©2003
+ Let p be a prime number congruent to 3 modulo 4. When p is less than 79: (a) x^2 - py^2 = 5 has integer solutions iff p is square modulo 5; (b) px^2 - y^2 = 7 has integer solutions iff p is square modulo 7. Curiously, 79 is the smallest p (and the only p less than 223) that does not follow the same rules. [Yosei]




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