A Thâbit ibn Kurrah prime, sometimes called a 321-prime, is a Thâbit ibn Kurrah number (i.e., a number of the form  for nonnegative integer ) 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 (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 Thâbit ibn Kurrah primes.

	digits	discoverer
		PrimeGrid (Dec. 2005; https://primes.utm.edu/primes/page.php?id=76506)
		PrimeGrid (Mar. 2007; https://primes.utm.edu/primes/page.php?id=79671)
		PrimeGrid (Apr. 2008; https://primes.utm.edu/primes/page.php?id=84769)
		PrimeGrid (Apr. 2010; https://primes.utm.edu/primes/page.php?id=92517)
		PrimeGrid (Nov. 2014; https://primes.utm.edu/primes/page.php?id=118807)
		PrimeGrid (Mar. 2015; https://primes.utm.edu/primes/page.php?id=119571)
		PrimeGrid (Jun. 6, 2015; https://primes.utm.edu/primes/page.php?id=120038)

REFERENCES:

Caldwell, C. https://primes.utm.edu/primes/search.php?Description=%5E3*2%5E%-1&Style=HTML.

PrimeGrid. "BOINC Status: Subproject Status: LLR: 321 Prime Search." https://www.primegrid.com/server_status_subprojects.php.

PrimeGrid. "PrimeGrid Primes: Subproject: (321) 321 Prime Search." https://www.primegrid.com/primes/primes.php?project=321.

Riesel, H. "Lucasian Criteria for the Primality of ." Math. Comput. 23, 869-875, 1969.

Sloane, N. J. A. Sequences A002235/M0545 and A055010 in "The On-Line Encyclopedia of Integer Sequences."

Underwood, P. "321 Statistics." 14 Dec 2004. https://www.mersenneforum.org/showthread.php?t=3410.

Underwood, P. "321 Search." https://www.mersenneforum.org/321search/.

Underwood, P. https://www.mersenneforum.org/321search/The%20status%20of%20the%20search.html.