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Stumpmaster

Stumpmaster

Well-Known Member 70 From Hamilton, New Zealand
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  • Stumpmaster
    Sequentially all prime numbers can be arranged in symmetrical strings. String 66 = 37 integers 840 to 876 and has primes 853, 857, 859, 863
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    MatthewG
    MatthewG
    Stumpmaster that is interesting.
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    where a pair of odd primes is said to be symmetric if each prime is congruent to one modulo their difference.
    so we're not talking about the common definition of 'symmetry' here

    in the example you gave, 853 & 857 are both congruent to 1 mod 4, and 857 & 859 are congruent to 1 mod 2, but 859 is 3 mod 4, and 863 is 3 mod 4. so it's not a symmetric string . . ?
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    is this what you were trying to say?

    'for every integer m at least 2 there is a string of m consecutive primes, any two of which form a symmetric pair."

    that statement is proven here:
    https://arxiv.org/abs/1908.06161
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