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1001, a Scheherazade palindrome !

1001 is the twenty-sixth pentagonal number ! 26*(3*26-1)/2 (Sloane's A000326)
1001 is the fourth palindromic pentagonal number.
See Sloane's A002069 : 1 , 5 , 22 , 1001 , ...
1001 is the product of three consecutive primes : 7 * 11 * 13

A nice finite pattern can be made with 1001
10011 = 1001
10012 = 1002001
10013 = 1003003001
10014 = 1004006004001

The following property of 1001 was discovered by [G. L. Honaker, Jr.]
General formulation : Prime p * Sum of the next p consecutive primes = a palindrome.
[ Dropping the palindrome condition gives sequence A036660. ]

1001 = 7 * (11+13+17+19+23+29+31) [Prime Curios!]
There exist a second palindrome with this property namely 3883
3883 = 11 * (13+17+19+23+29+31+37+41+43+47+53) [Prime Curios!]
Both the prime and the sum of primes of this last solution are palindromic primes !
3883 = 11 * (353)

Who can find the third palindromic solution ?


The largest (probable) prime of  326, 3191, 3419, etc. digits is made with
1001 as the negative displacement from those power of ten axes
103261001
1031911001
1034191001
1035461001
1078661001
10121891001
10126871001
10151321001
10151671001
10163661001
10181381001




A000031 Prime Curios! Prime Puzzle Richard Phillips
Wikipedia 31 Le Nombre 31 Numberland 31














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