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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Just showing those entries submitted by 'Beedassy': (Click here to show all) The smallest prime that divides a 7digit number of the form p0p, where p is any 3digit prime. [Beedassy]The largest known prime that starts a chain (generated by the quadratic 73  x  x^{2}, for x = 0, 1, 2, ... , 7) of smaller, increasingly distant primes with successive gap 2n, (n = 1, 2, 3, ..., 7): 73, 71, 67, 61, 53, 43, 31, 17. [Beedassy] The smallest prime with prime digits that belongs both to an emirp pair (37, 73) and to a twin prime pair (71, 73) as the larger member. [Beedassy] The smallest prime that is the middle term of three consecutive numbers each expressible as a sum of two nonzero squares: 72 = 6^{2} + 6^{2} ; 73 = 3^{2} + 8^{2} ; 74 = 5^{2} + 7^{2}. Note that replacing the first prime digit 7 by the prime 23 forms instead the smallest prime (233) that is the middle term of three consecutive numbers each expressible as a sum of two distinct nonzero squares: 232 = 6^{2} + 14^{2} ; 233 = 8^{2} + 13^{2} ; 234 = 3^{2} + 15^{2}. [Beedassy] 73 is the only Sheldon prime, i.e., i) whose binary representation is palindromic (1001001_{2}) and ii) which belongs to an emirp pair (P_{n}, P_{m}) such that subscripts (m, n) = (21, 12) are also reversals of each other and n has a prime decomposition 21 = 3*7 that concatenates back to P_{m} (Carl Pomerance, Chris Spicer, February 2019). [Beedassy]
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