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**

**1001**^{1} = **1001**

**1001**^{2} = **1002001**

**1001**^{3} = **1003003001**

**1001**^{4} = **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

**10**^{326} — **1001**

**10**^{3191} — **1001**

**10**^{3419} — **1001**

**10**^{3546} — **1001**

**10**^{7866} — **1001**

**10**^{12189} — **1001**

**10**^{12687} — **1001**

**10**^{15132} — **1001**

**10**^{15167} — **1001**

**10**^{16366} — **1001**

**10**^{18138} — **1001**