By replacing the 1st digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime. By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property. Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.

(In other words: the smallest prime of the family contains one digit, or a larger number of identical digits, which, when replaced with another digit or other identical digits, fills out the family to eight members.) Project Euler problem 51

(In reply to Just a comment! by Charlie)

Problems 1 to 50 are rated at 5% difficulty. Yes, #51 is tougher, and is rated at 15%. Beyond #51, the problems have a rising range of difficulty starting with a 5-25% range, but eventually the top of the range reaches 100% toward the end of the current span of 876 problems. 

Edited on February 16, 2024, 12:35 pm

Posted by Steven Lord on 2024-02-16 12:26:38