Problems & Puzzles: Puzzles

Puzzle 17.- Weakly Primes

Following the problem 12 of the "South Missouri State University archive of puzzles" ( http://math.smsu.edu/~les/POW12.html ), a weakly prime is any prime that lost his primality condition by changing - one at a time-anyone of it’s digits to any number (0-9) other than the current.

In base 10 the first 3 weakly primes are : 294001, 505447, 584141.

I’ll keep here the first one and the 10 largest weakly primes base 10 :

 Weakly Primes base 10 The first 294001(Obtained by Ken Duisenberg) The 10 largest 18 999999999997802311 J. McCranie (17/08/98) 18 999999999998270057 "" 18 999999999998832431 "" 21 999999999999999543767 Robert T. McQuaid 50 (9)44 649691 C. Rivera 61 1(0)53 2236743 C. Rivera 81 1(0)73 1295823 C. Rivera 101 1(0)94 590181 C. Rivera 151 1(0)144 366303 C. Rivera 201 1 (0)193 3592453 C. Rivera 251 1 (0)243 1856301 Tiziano Mosconi 23/8/01

On March 2007, J. K. Andersen wrote:

A 1000-digit weakly prime: (17*10^1000-17)/99+21686652 = (17)_496 38858369. Found with PrimeForm/GW and proved with Marcel Martin's Primo.

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