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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