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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 77! + 1 is prime! 77 contains 'Lucky 7 and 11' as prime factors. [Sladcik] The square of 77 is 5929, the concatenation of two primes, 59 and 29. [Trotter] The concatenation of all palindromes from one up to 77 is prime. [De Geest] The number 7^7+77^7+777^7+2 is prime with digital sum 77. [Patterson] 77 is equal to the sum of the first 8 primes. Note it is also the product of the middle two numbers of this sequence (11*7 = 77). [Kazgan] 77^77*78^781 is the only nontitanic prime of form a^a*b^b1, where a, b are successive numbers that are both composite. [Loungrides] Prime numbers that end with "77" occur more often than any other 2digit ending among the first one million primes. [Gaydos] There are 77 primes that never enter the repdigit sequence 1, 31, 331, 3331, 33331, etc. as factors. The sequence has general nth term s(n) = (10^n7)/3 and the primes correspond to n = 3, 5, 7, 11, 13, 37, 41, 43, 53, 61, 67, 71, 73, 79, 89, 101, 103, 107, 127, 137, 139, 151, 157, 163, 173, 191, 211, 239, 241, 251, 271, 277, 281, 293, 317, 347, 349, 359, 397, 409, 443, 449, 457, 521, 547, 599, 601, 613, 617, 631, 641, 643, 677, 683, 691, 733, 739, 751, 757, 761, 769, 773, 797, 827, 853, 859, 881, 883, 907, 911, 919, 929, 947, 967, 991 and 997. [Schiffman] 77 is probably the maximal quantity of integers less than 100 that can be arranged in a row such that each is a multiple or a divisor of its neighbors. The solutions is not unique. Here is one due to Dmitry Kamanetsky: 62 31 93 1 57 19 76 38 2 52 26 13 39 78 6 54 27 81 9 63 21 42 84 28 56 14 98 49 7 77 11 99 33 66 22 44 88 8 48 12 36 18 72 24 96 32 64 16 80 40 20 100 50 25 75 15 45 90 30 60 10 70 35 5 85 17 34 68 4 92 46 23 69 3 87 29 58. Missing: 37 41 43 47 51 53 55 59 61 65 67 71 73 74 79 82 83 86 89 91 94 95 97. Can you find a better solution, using 78 or more terms? [Rivera]
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