Problems & Puzzles: Puzzles

 Puzzle 432. A nice pattern with 6 consecutive primes. JM Bergot found the following nice pattern involving 6 consecutive primes (from 11 to 29) producing 5 primes (167, ...., 719) 11x13 + 11 + 13=167, PRIME 13x17 + 13 + 17=251, PRIME 17x19 + 17 + 19=359, PRIME 19x23 + 19 + 23=479, PRIME 23x29 + 23 + 29=719, PRIME 29x31 + 29 + 31=959 Composite Carlos Rivera found an example involving 7 consecutive primes: 254908033, 254908037, 254908063, 254908097, 254908099, 254908109, 254908117. Question: Find a larger example?

Jan van Delden & Farideh Firoozbakht found the same solution for 8 consecutive primes:

5823417569, 5823417619, 5823417623, 5823417647, 5823417659, 5823417667, 5823417683, 5823417709

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Giovanni Resta wrote (Apr. 08):

The first two patterns involving 9 primes start at the primes 3,889,108,085,627 and 4,391,510,905,303. The smallest one is about 667 times greater than the prime at which the smallest pattern of 8 primes start, i.e., 5,823,417,569.

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