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An original puzzle from Enoch Haga involving primes
[ March 1999 ]

 Find more palindromes that are the concatenation of the nth prime with 
the sum of the primes smaller or equal to this nth prime.

Enoch Haga himself discovered two nice solutions for this hard problem.

At 73, the 21st prime, the sum of the primes <= 73 is 712
from which the palindrome 21712 is formed.
At 4177, the 574th 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 con-cat-enate!
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 :

 PNSPP
N & S73
4177
21
574
712
1111475
21712
5741111475
S & N????
N & P17
183661
61241363
7
16638
3631421
 717
16638183661
363142161241363
P & N491
1823
6883
757063
9642461
329147719
94
281
886
60757
642469
17741923
 49194
1823281 (prime curios!)
6883886
75706360757
9642461642469
32914771917741923
P & S2
7
1
4
2
17
22
717
S & P21222


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