Problems & Puzzles: Puzzles

 Puzzle 745. A number 20 digits large, best qualified Here we ask you to get a 20 digits integer N having two digits of each from 0 to 9 such that for each prime string of large L inside it you are able to add L to the qualification of N. Q. Get your best qualified N integer a) Reading the primes only from left to right. b) Reading the primes in both directions. Please send only you best qualified integer N for each question and the corresponding primes.

Contributions came from Emmanuel Vantieghem

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Emmanuel wrote:

My best qualified  N  is  26248504586017971933  with  L = 333  and prime set :
{2, 3, 5, 7, 17, 19, 71, 79, 97, 179, 193, 601, 719, 797, 971, 1933, 7193, 9719, 17971, 58601, 71933, 86017, 179719, 971933, 1797193,
4586017, 6017971, 45860179, 60179719, 4850458601, 24850458601, 58601797193, 4850458601797, 48504586017971, 50458601797193,
248504586017971, 485045860179719, 504586017971933, 2624850458601797, 6248504586017971, 8504586017971933, 48504586017971933,
624850458601797193, 6248504586017971933}
But I'm sure there are better ones.

My best qualified  N  for double read direction is  17336845640852029719  with  L = 393  and prime set :

{2, 3, 5, 7, 17, 19, 29, 37, 71, 73, 79, 97, 173, 179, 337, 719, 733, 863, 971, 1733, 2029, 2971, 3371, 6337, 9719, 20297, 520297, 4863371,
5202971, 654863371, 5640852029, 8046548633, 40852029719, 456408520297, 845640852029, 5640852029719, 20258046548633,
25804654863371, 92025804654863, 336845640852029, 684564085202971, 2025804654863371, 3684564085202971, 6845640852029719,
73368456408520297, 79202580465486337, 91792025804654863, 92025804654863371, 7336845640852029719, 9179202580465486337}
Also, I'm sure there are better ones.

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