21888242871839275222246405745257275088548364400416034343698204186575808495617

21888242871839275222246405745257275088548364400416034343698204186575808495617 is a 254‑bit prime that serves as the prime modulus p for the BN254 (also known as altBN128) elliptic-curve, pairing-friendly family used in modern cryptography. This prime defines the finite field F_p over which the BN254 curve is constructed. The curve, together with its associated subgroup structure, enables efficient implementations of bilinear pairings, a key tool in many cryptographic protocols.

In the BN254 construction, elliptic curves defined over F_p support a pairing e that maps pairs of points from two groups into a third group, preserving certain algebraic properties. The BN254 family is designed to have a large prime order subgroup, often denoted r, and a pairing with relatively fast computation. The combination of a suitable p and r makes the curve suitable for zero-knowledge proofs, attribute-preserving cryptography, and other protocols that rely on bilinear maps.

Because of its efficiency and security properties, BN254/altBN128 has seen widespread adoption in practice. It is used in zk-SNARK implementations, various cryptographic libraries, and blockchain systems that require succinct, non-interactive proofs and verifiable computations. In Ethereum, the BN128 (bn256) family is referenced in relation to precompiled contracts that perform pairing checks, enabling practical verification of complex proofs on-chain.

See also: BN254, altBN128, pairing-based cryptography, zk-SNARKs, elliptic curves, cryptographic primes, Ethereum BN128 precompiles.