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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The word 'PRIMETEST' is prime when written in radix 36 using 'A'=10, 'B'=11, ... 'Z'=36. In decimal this number is 72684117341741. [Caldwell] The exact number of ways to partition the integer 36 is prime. The smallest number which is the sum of two distinct odd primes in four ways (36 = 5 + 31 = 7 + 29 = 13 + 23 = 17 + 19). [McCranie] The smallest square that is the sum of a Twin prime pair {17, 19}. [Trotter] The smallest number expressible as the sum of consecutive primes in two ways (5 + 7 + 11 + 13 and 17 + 19). [De Geest] The smallest multidigit number such that both 36*63+1 and 36*631 are prime. [Gupta] The smallest triangular number whose sum of divisors as well as sum of aliquot divisors is also a triangular number. [Gupta] The smallest power (greater than 1) which is not a prime power. [Gupta] The smallest even number that cannot be expressed in any of these forms: 2^{n}, 2^{n}p, with p an odd prime, p+1 with p an odd prime (e.g., 36 = 2^{2}3^{2}, 36 = 35 + 1, but 35 is not prime). [Rodrigo] The smallest square n such that if you square the n first prime numbers and add them up, the result is a prime number. [Capelle] 5+7+11+13 is the smallest square number expressible as the sum of four consecutive primes which are also two couples of prime twins! [Herault]
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