17976931348623157

17976931348623157 is a 17‑digit integer notable in number theory for being a prime number that lies just below the power of two 2⁵⁴ (18 014 398 509 481 984). It is the largest known prime smaller than 2⁵⁴ and consequently the greatest prime with fewer than 18 decimal digits. The number is odd, ends in the digit 7, and has no trivial divisors; trial division up to its square root confirms its primality. Its prime status makes it a reference point in listings of consecutive prime gaps and in studies of the distribution of primes near large powers of two.

The integer appears in various computational contexts. In cryptographic literature it is sometimes cited as an example of a modest‑size prime suitable for testing modular arithmetic algorithms, such as modular exponentiation and primality‑testing routines. Because its magnitude is comfortably within the range of 64‑bit arithmetic, it serves as a benchmark value for evaluating the performance of integer‑handling libraries on modern processors.

Mathematically, 17976931348623157 does not belong to any special prime families such as Mersenne, Fermat, or Sophie‑Germain primes, nor is it known to be a member of a larger known pattern. Its factorization is trivial, consisting solely of itself and the unit. The number also marks a boundary in prime‑gap tables: the gap between the preceding prime 17976931348623149 and 17976931348623157 is eight, while the subsequent prime 17976931348623171 creates a gap of fourteen, illustrating the irregular spacing of primes in this region.

Although the numeral itself carries no particular historical or cultural significance, its role as the largest prime below 2⁵⁴ makes it a convenient reference in theoretical discussions about prime density, computational limits of 64‑bit number spaces, and performance testing of algorithms that handle large integers.