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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The larger of the only two primes resulting from concatenation of two twodigit primes, each of them formed from two consecutive digits. [Silva] The least prime p such that for all 2^k < p the numbers p + 2^k, p  2^k, p*2^k + 1, and p*2^k  1 are composite. [Wesolowski] The largest distinctdigit prime, concatenated from two doubledigit primes, such that, αlternating the 2nd and 4th digits we create another prime, also concatenated from two doubledigit primes, i.e., 8329. Note that there is only another such case, i.e., (3761, 3167). [Loungrides]
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