WON plate | World!OfNumbers 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 10326 – 1001 103191 – 1001 103419 – 1001 103546 – 1001 107866 – 1001 1012189 – 1001 1012687 – 1001 1015132 – 1001 1015167 – 1001 1016366 – 1001 1018138 – 1001 A000031 Prime Curios! Prime Puzzle Richard Phillips Wikipedia 31 Le Nombre 31 Numberland 31
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