[ March 1999 ]
An original puzzle involving primes
Enoch Haga
Find more palindromes that are the concatenation of the n^{th} prime with the sum of the primes smaller or equal to this n^{th} prime. 
Enoch Haga himself discovered two nice solutions for this hard problem.
At 73, the 21^{st} prime, the sum of the primes <= 73 is 712
from which the palindrome 21712 is formed.
At 4177, the 574^{th} prime, the sum of the primes <= 4177 is 1111475
from which the palindrome 5741111475 is formed.
Apparently not easy to find, Enoch dares to challenge you to find more solutions !
"I have now checked to 199909, the 17978^{ th} prime, and found nothing else to concatenate!
Perhaps there are no more, but then I shall offer a prize of $5.95
(the sum of 21 and 574 divided by 100  just because it forms a palindrome)
to anyone discovering the next one in sequence (or who proves that it is impossible)."
[ August 15, 2002 ]
Jean Claude Rosa distinguished more cases that could be examined.
Let P be the prime number, N its rank number,
S the sum of the prime numbers < = P,
& the concatenation operation and
PP the result that must be palindromic.
JCR proposes the following six 'equations' to solve !
N & S = PP (Enoch's puzzle)
S & N = PP
N & P = PP
P & N = PP
P & S = PP
S & P = PP

By varying P from 2 up to 1175497783 JCR obtained the following
results :
 P  N  S  PP 
N & S  73 4177  21 574  712 1111475  21712 5741111475 
S & N  ?  ?  ?  ? 
N & P  17 183661 61241363  7 16638 3631421   717 16638183661 363142161241363 
P & N  491 1823 6883 757063 9642461 329147719  94 281 886 60757 642469 17741923   49194 1823281 (prime curios!) 6883886 75706360757 9642461642469 32914771917741923 
P & S  2 7  1 4  2 17  22 717 
S & P  2  1  2  22 