Problems & Puzzles: Puzzles

Puzzle 1154 Consecutive primes over a replacement system Dmitry Kamenetsky sent the following nice puzzle: Suppose we have the following replacement system. We replace every 0 with 6, every 1 with 4, every 2 with 7 and so on like so: 0->6, 1->4, 2->7, 3->9, 4->5, 5->2, 6->6, 7->8, 8->10, 9->3    Note that 8 is replaced with 2 digits (10). Now if we start with 19 then we can obtain the following 18 primes:   19 43 59 23 79 83 109 463 569 263 769 863 1069 4663 5669 2663 7669 8663   Q. Is it possible to find a replacement system and a starting number that produces more than 18  primes?

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On 28 Dec 2023, Gennady Gusev wrote:

I found the chain of 19 primes from 503:

503, 283, 463, 173, 593, 2203, 4483, 1163, 5573, 2293, 44203, 11483, 55163, 22573, 44293, 114203, 551483, 225163, 442573

with such replacement system:

0->8, 1->5, 2->4, 3->3, 4->1, 5->2, 6->7, 7->9, 8->6, 9->20

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