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WON plate
143 |


[ November 12, 2002 ]
Palindromic Primes stretching out until...
by Jeff Heleen (email)


I have found 3 palprimes. I don't know if you have them
somewhere already on your site but here they are.
If you start with a central 1 and concatenate the
counting integers to either side (mirrorwise to the left),
the palprimes occur at N = 31, 59 and 113,
all three N values are coincidentally prime !

1303928272...7654321234567...2728293031 = prime (105 digits)
9585756555...7654321234567...5556575859 = prime (217 digits)
311211111011...4321234...110111112113 = prime (417 461 digits)

My search went up to N = 999. I used Primo for the tests.

Who can extend this list with a few more terms ?

[November 15, 2002 ]
Jean Claude Rosa wrote that the third number
had a wrong length indication 417 instead of 461.
"Soit P = n... ...32123... ...n avec 99 < n < 1000
pour avoir la longueur de P j'utilise la formule suivante :
longueur de P = 6 * n - 217
Si n = 113, longueur de P = 6 * 113 - 217 = 461.
"

[November 17, 2002 ]
Jeff Heleen has another possible palprime for this plate.
For N = 1277 (a prime itself) shows promise. This would yield
a number with 8001 digits (assuming I have added correctly).
I shall not attempt to prove it prime at this time as it
would take far too much time.

PDG tested this candidate with PFGW [July 13, 2004 ]
but to my surprise the outcome was that this number is composite !
In case I made a mistake perhaps someone would like
to confirm that this palindrome is not a probable prime ?




A000143 Prime Curios! Prime Puzzle
Wikipedia 143 Le nombre 143














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