PRP Proof File Spec

The PRP Proof format described below represents the consensus reached by the GIMPS project. This allows proofs to be produced and consumed by various software such as mprime/Prime95 and GpuOwl and hopefully others.

The file starts with an ASCII section composed of a few lines separated by a single '\n' character. Example header:

PRP PROOF\n
VERSION=1\n
HASHSIZE=64\n
POWER=9\n
NUMBER=M216091\n

This ASCII header is immediately followed by a number of binary residues, in total POWER + 1 residues. Each of these residues is represented as a series of bytes, starting with the least-significant byte. The size in bits of a residue is derived from the NUMBER information in the header (for example, a residue modulo a mersenne number such as M216091 is has 216091 bits), and the number of bytes in the persistent form of a residue is the minimum number of bytes that covers the bit-size of the residue.

The residues

The header section is followed immediately by N+1 (where N is the proof power) binary residues without separators.

A residue is a value modulo the Mersenne candidate 2^E-1. As such, a residue has exactly E bits. A residue is stored as a sequence of bytes starting with the least-significant byte. The number of bytes of a residue is (E-1)/8+1.

The first residue is called B and is the PRP residue at iteration topK. The next N residues are called middles, denoted M[0]...M[N-1]. More details about the meaning of these residues is found in Proof Verification.

The proof covers the iteration range up to iteration topK -- it allows to verify the correctness of the residue at topK (B). The implicit value topK is the lowest multiple of 2^POWER that is larger than E.

An example proof file is provided.