Problems & Puzzles: Puzzles

Puzzle 781. A second follow-up to Puzzle 776 Here we will ask for primes p that generate k primes p→ {p1, p2, ...pi... pk} following a variation of the basic rule of puzzle 776: pi=p+Σ(dj^i)p, for i=1 to k Carlos Rivera found a prime that generates 10 primes: k=10, p=2237051 2237051→ {2237071, 2237143, 2237563, 2240191, 2257291, 2371183, 3141163, 8399551, 44564491, 294539023} 2237071 = 2237051+ 2^1+2^1+3^1+7^1+0^1+5^1+1^1 2237143 = 2237051+ 2^2+2^2+3^2+7^2+0^2+5^2+1^2 ... 294539023 = 2237051+ 2^10+2^10+3^10+7^10+0^10+5^10+1^10 Q. Send your prime p with the largest set of k>10 primes thus generated.

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Contribution came from Jan van Delden

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Jan wrote:

I found five solutions for k=11: 49970564789, 83335433567, 134202899431, 195279409453, 491128662911.

 

One solution for k=12: 962787043927, generating the following primes:
 

[962787043991,962787044369,962787047249,962787070013,962787254321,

962788773509,962801476409,962908961213,963827524001,971743356149,

1040438250569,1640083554413]

 

I feel like I’m missing a “trick” to limit the search..

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