Problems & Puzzles: Puzzles

Puzzle 190. A follow up for the puzzle 188

Maybe is worthwhile to read first the Puzzle 188.

Here you are asked to seek for these n values such that:

  • n is prime
  • n divides S where S is the concatenation of the first n natural numbers

Jeff Heleen, who proposed this follow up, has gotten the first 5 solutions: n = 2, 3, 5, 8167 & 371321.

BTW, S(371321) is a number having 2,116,821 decimal digits

Question: Find 3 more solutions.

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Note: if n is not asked to be prime,  then the corresponding sequence is the EIS A029455, by Olivier Gerard.

 

Solution:

Jens Kruse Andersen wrote (24/9/2002): " I have tested all primes below 20 million with an efficient C program using inline assembler. The program reached the biggest known solution 371321 in 3.5 minutes and then ran for several days. I only found the known solutions. This looks hard unless someone can find a clever shortcut".

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