A Thābit ibn Qurra prime, sometimes called a 321-prime, is a Thābit ibn Qurra number (i.e., a number of the form 
for nonnegative integer 
) that is prime.
The indices for the first few Thābit ibn Qurra 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 (1969) extended the search to 
. A search for larger primes was coordinated by P. Underwood.
PrimeGrid has continued that search and has checked values of 
up to 
as of Nov. 2015 (PrimeGrid). The table below summarizes
the largest known Thābit ibn Qurra primes.
 | digits | discoverer |
 |  | PrimeGrid (Dec. 2005; https://t5k.org/primes/page.php?id=76506) |
 |  | PrimeGrid (Mar. 2007; https://t5k.org/primes/page.php?id=79671) |
 |  | PrimeGrid (Apr. 2008; https://t5k.org/primes/page.php?id=84769) |
 |  | PrimeGrid (Apr. 2010; https://t5k.org/primes/page.php?id=92517) |
 |  | PrimeGrid (Nov. 2014; https://t5k.org/primes/page.php?id=118807) |
 |  | PrimeGrid (Mar. 2015; https://t5k.org/primes/page.php?id=119571) |
 |  | PrimeGrid (Jun. 6, 2015; https://t5k.org/primes/page.php?id=120038) |
." Math. Comput. 23, 869-875, 1969.Sloane,
N. J. A. Sequences