Problems & Puzzles: Puzzles

 Puzzle 456. Mersenne Primes as a sum of consecutive primes Anton Vrba sent the following puzzle proposal:  2^5-1 = 7+11+13 2^17-1 = 43669 + 43691+ 43711 2^127-1 = 56713727820156410577229101238628035201 + 56...243 + 56...283 Q. Express Mersenne Primes as a sum of consecutive primes

Carlos Rivera wrote on July 10, 2020

The 5th Mersenne prime, 2^13-1=8191 is the sum of 13 primes, The 1st = 599 and the 13th = 661

The 9th Mersenne prime, 2^61-1=2305843009213693951 is the sum of 175 primes, The 1st = 13176245766932173 and the 175th = 13176245766938521.

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On Set 19, 2020, Adam Stinchcombe wrote:

2^7-1 is the sum of 9 consecutive prime from 3 to 29

2^17-1 is not only the sum of 3 consecutive primes, but also the sum of 31 consecutive prime from 4099 to 4357

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