Problems & Puzzles: Puzzles

Problem 89. Palindromic binary expression of primes squared

This nice story started with Patrick De Geest in 1999. He found that the square of the prime 295742437 is 87463589042698969 that has a palindromic binary representation: 100110110101110111010101110111011101010111011101011011001

(See OEIS A003166)

Twenty years later, Dec 10, 2019, Michael Coriand, found, that the square of the prime 1229661818323605647753 is 512068187442916142366763805165638713949009 -> 10001010110111001000110101100000000111110000111010000011010111010011111111100101110101100000101110_
0001111100000000110101100010011101101010001 (Palindrome).

(See https://oeis.org/A003166/b003166.txt)

I can not tell if Coriand was aware that 1229661818323605647753 was the largest prime found at the moment of his publication. I tested the primality of the published integers in b003166,txt table, in reverse order and stopped in 1229661818323605647753, bingo is prime!
 

Q1. What other primes of this type are on the table https://oeis.org/A003166/b003166.txt

Q2. Find the next larger prime of this type

 


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