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] [MarieSophie Germain (17761831)]
[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 9digit 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
