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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The first 65 digits of 65^{65} form a prime number. [Honaker] The product of the first two primes of the form 4n + 1. Euler found 65 integers, which he called "numeri idonei," that could be used to prove the primality of certain numbers. [Brown] 6^{65}  5 is the smallest prime of the form a^{c}  b, where b = a  1. Note that c is the concatenation of a and b. [Kulsha] The smallest composite number of the form n^{2} + 1, where n is even. 65 is the ONLY number which gives a prime square, on adding as well as subtracting its reverse from it (65 + 56 = 11^{2}, 65  56 = 3^{2}). [Gupta] The only number which is the difference of fourth powers of two primes. [Murthy] (65!)^{2} + 1 is prime. [Dobb] 65 = 5 * 13 and (65) = (5) * (13) = 5 + 13. [Honaker] The smallest Fermat semiprime. [Capelle] (65) = phi(65)  6*5. [Langroudi]
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