[ *January 10, 2005* ]

Nearest (probable) primes bordering powers of ten

situated at equal distances

10^{17} ± **3**

10^{45} ± **9**

10^{3175} ± **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 ! )

10^{16989} + **1777771**

10^{18510} + **1777771**

10^{25173} + **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** ?