[ *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 ?