A Thābit ibn Qurra prime, sometimes called a 321-prime, is a Thābit ibn Qurra number (i.e., a number of the form 
for a 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 large Thābit ibn
Qurra primes reported through 2025.
S. Brown found the Thābit ibn Qurra prime 
as part of PrimeGrid on Jun. 25,
2025. It has 6,971,216 decimal digits and is listed
as proven by PrimePages (PrimeGrid 2025, PrimePages 2025).
."
2025. 
." Math. Comput. 23, 869-875, 1969.Sloane,
N. J. A. Sequences