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A Prime Number Case to Consider

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  • w_sindelar@juno.com
    Consider these 4 prime numbers namely, A= 1049681, B= 1049683, C= 1049861, D= 1049863. Some interesting facts are: One, A and B are twins. C and D are twins
    Message 1 of 2 , Jan 8, 2013
      Consider these 4 prime numbers namely, A= 1049681, B= 1049683, C= 1049861, D= 1049863. Some interesting facts are: One, A and B are twins. C and D are twins and the pair (A, B) and the pair (C, D) are consecutive twin pairs. Two, the digits that define A are the same as the digits that define C and they sum to the twin 29. The digits that define B are the same as the digits that define D and they sum to the twin 31. Three, the sum of the digits that define he product of 29 and 31 namely 899, is 26. The sum of the digits that define the product of A and B namely, 1101832301123 is also 26. The sum of the digits that define the product of C and D namely, 1102210219043 is again 26, and 26 equals 2 times the twin 13. Four, the difference between the middle numbers of the twins (A. B) and (C, D) is 180, which is the middle number of the twin pair (179, 181). Five, the sum of the digits that define the sumof A, B, C and D namely, 4199088 is 39 and 39 is the product of twins 3 and 13. My best wishes to everyone for 2013. Prime number 2013 is 17491 whose digits sum to 22, which is the product of 2 and the twin 11. And the twin 13 plus 2000, H'm, ok I'll quit. Thanks folks. Bill Sindelar
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    • Jens Kruse Andersen
      ... Consider these 8 consecutive primes: 18948901076698271690467136006698708653641386544429 1475408862860716126025520041510000 + n, for n = 0121, 0123, 0211,
      Message 2 of 2 , Jan 8, 2013
        Bill Sindelar wrote:
        > Consider these 4 prime numbers namely, A= 1049681, B= 1049683,
        > C= 1049861, D=1049863. Some interesting facts are: One, A and B
        > are twins. C and D are twins and the pair (A, B) and the pair
        > (C, D) are consecutive twin pairs. Two, the digits that define A
        > are the same as the digits that define C and they sum to the twin
        > 29. The digits that define B are the same as the digits that
        > define D and they sum to the twin 31.

        Consider these 8 consecutive primes:
        18948901076698271690467136006698708653641386544429\
        1475408862860716126025520041510000 + n,
        for n = 0121, 0123, 0211, 0213, 1021, 1023, 1201, 1203

        They form four consecutive twin prime pairs where the lower twin
        members (n = 0121, 0211, 1021, 1201) contain the same digits,
        and so do the upper members (n = 0123, 0213, 1023, 1203).

        The smallest possible width in such a constellation is 1082 like
        in the above 84-digit example. The requirement for 1075 composite
        numbers would make it harder to find a small example.

        --
        Jens Kruse Andersen
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