A beautiful cryptic prime curio about palprimes 191 & 383

G. L. Honaker, Jr.

Let A = 1, B = 2, C = 3, etc. [More info at Puzzle 33 from Carlos Rivera's PP&P website]

PALINDROMES ARE FUN *My most favourite axioma!*

P+A+L+I+N+D+R+O+M+E+S+A+R+E+F+U+N

The sum of these letters is **191** a palindromic prime !

The palindromic prime **15551** written out in English words :

FIFTEEN THOUSAND FIVE HUNDRED FIFTY ONE

F+I+F+T+E+E+N+T+H+O+U+S+A+N+D+F+I+V+E+H+U+N+D+R+E+D+F+I+F+T+Y+O+N+E

These letters add to **383** again a palindromic prime !

(**15551** is the 'smallest' palprime with this property.)

A neat fact is that **191** & **383** form the lowest

threedigit Palindromic Sophie Germain Prime pair.

2(**191**)+1 = **383**

Concatenate all the threedigit palprimes without **191**

101_131_151_181_313_353_373_383_727_757_787_797_919_929

and you'll find that this number is divisible by **383** !

Visit also Eric W. Weisstein's page about Sophie Germain Primes !

[Women in Math] [Sloane A005384] [Marie-Sophie Germain (1776-1831)]

[Sophie Germain Primes] [Palindromic Sophie Germain Primes]

[Yves Gallot's Proth.exe and Cunningham Chains]

A result from Carlos Rivera's work on adding the letters of written_out numbers

(in English) is that he proved that these two 9-digit numbers are equal !

123456789 = 987654321

Please visit my Nine Digits Page to see how he came to this conclusion !

Another less known fact is that **383** divides

the Mersenne number 2^{191} – 1