Another New Record Near-repdigit Palindromic Prime

10^314727-8*10^157363-1 is prime. Here's the link to the Prime Pages. Here is the link to the PWP website. Here's the link to Patrick De Geest's table of near-repdigit palindromic primes, or "Palindrome Wing Primes."

New World Record Near-repdigit Palindrome Prime

The base ten near-repdigit palindrome 10^290253-2*10^145126-1 is a prime number. It's the largest known palindromic prime, and only the second known prime of the form 10^(2*x+1)-2*10^x-1 (correction: for x>0).

Written out, it's 145126 nines, a seven, and 145126 more nines.

Leap Day Near-repdigit Palindrome Prime!

10^269479-7*10^134739-1 is prime! This is a new world record for near-repdigit palindrome primes. It is also the second largest known palindromic prime and one of the top twenty largest near-repdigit primes (as of the date of discovery, February 29, 2012).

Another world record near-repdigit palindrome prime

After I found the previous one on Halloween, another one turns up the day before Thanksgiving. This one is all nines, except for the center digit which is eight.

Primality testing 10^(2*67404+1)-1*10^67404-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^(2*67404+1)-1*10^67404-1 is prime! (4490.0911s+0.0381s)

(It's better written out as 10^134809-10^67404-1 ).

7*(10^3891-1)/9-5*10^1945 is prime

The Primo certificate for 7*(10^3891-1)/9-5*10^1945 is here.

7*(10^4489-1)/9-2*10^2244 is prime.

Here's the Primo certificate for 7*(10^4489-1)/9-2*10^2244.

New world record near-repdigit palindrome prime

I got a treat for Halloween:

Primality testing 10^(2*62938+1)-7*10^62938-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^(2*62938+1)-7*10^62938-1 is prime! (4195.7527s+0.0051s)

(It can also be expressed as 10^125877-7*10^62938-1)

This is the largest known near-repdigit palindrome prime number. Written out, it's a long string of 9's, a 2, and another long string of 9's.