321 prime

A Thâbit ibn Kurrah prime, sometimes called a 321-prime, is a Thâbit ibn Kurrah number (i.e., a number of the form 3·2^n - 1 for nonnegative integer n) that is prime. The indices for the first few Thâbit ibn Kurrah primes are 0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, ... (OEIS A002235), corresponding to the primes 2, 5, 11, 23, 47, 191, 383, 6143, ... (OEIS A007505). Riesel extended the search to n<=1000. A search for larger primes was coordinated by P. Underwood. PrimeGrid has continued that search and has checked values of n up to 12078521 as of Nov. 2015 (PrimeGrid). The table below summarizes the largest known Thâbit ibn Kurrah primes.

integer sequence primes | Thâbit ibn Kurrah number