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Some prime sequences (Posted on 2018-07-04) Difficulty: 3 of 5
What numbers N are the sum of a sequence of consecutive primes such that the product of the first and last numbers in the sequence is N?

No Solution Yet Submitted by Ady TZIDON    
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re(2): The sequence | Comment 9 of 11 |
(In reply to re: The sequence by Charlie)

I do see a notation that a later member of one of the sequences, A055233, Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor,

does in fact satisfy the requirements of the present puzzle. To quote the OEIS,  Its sixth member a(6): 454539357304421 is the product of two primes, 3536123 * 128541727 and also the sum of these two plus all the primes in between: 3536123 + 3536129 + 3536131 + ... + 128541719 + 128541727.

even though that sequence's fifth member,  2935561623745 = 5*19*53*61* 9557887, is not a semiprime and therefore doesn't fit this puzzle.

Edited on July 5, 2018, 8:50 pm
  Posted by Charlie on 2018-07-05 20:48:46

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