[ January 10, 2005 ]
Nearest (probable) primes bordering powers of ten
situated at equal distances

10¹⁷ ± 3
10⁴⁵ ± 9
10³¹⁷⁵ ± 13431

Only three pairs are known so far and all have palindromic
displacements. (despite the first two being a bit trivial)

Can you discover the fourth pair ?

Note that between the minus and plus values
a prime gap must exist obligatory.

Powers of Ten in the real world
from the macro- to the micro-universe
Cosmic View, the Universe in 40 Jumps

Coincidences around palindrome 13431

13431 can be expressed as the product
of two consecutive palindromes (111 * 121)

13431 is a palindrome n such that 10n01 is a prime. (A099744)

Jason Earls submitted to the PRP Record site these curious numbers:
( beware however that they are not borderprp's ! )

10¹⁶⁹⁸⁹ + 1777771
10¹⁸⁵¹⁰ + 1777771
10²⁵¹⁷³ + 1777771

Note that 1777771 is a PDP or a Plateau Prime.
Can you extend the list and/or find prp's of the form 10^x – 1777771 ?