Computation and Cryptographic Fingerprinting of a 109-Million-Digit Integer in the Q_59 Polynomial Family

This paper documents the successful computation of an extremely large integer generated by the polynomial Qₙ(q) = qⁿ − (q−1)ⁿ at specific parameters n=59 and q=10^1886792 + 3. The resulting value contains precisely 109,433,938 decimal digits, exceeding the Electronic Frontier Foundation's 100-million-digit prime number prize threshold. We provide the SHA-256 cryptographic fingerprint (A462032F37DC907EDEF64A575696EC0B11C052B42B469C76F6A6577B841864EF) to establish unique identity and enable independent verification. This work represents a computational achievement in handling ultra-large integers and serves as a foundation for future primality verification efforts. We emphasize that primality testing has not yet been performed on this number; it remains a candidate requiring rigorous verification through distributed computational resources. The paper includes detailed methodology, hardware specifications, and an explicit call for collaboration from institutions with supercomputer access. If successfully verified as prime, this candidate would represent a potential qualification for the Electronic Frontier Foundation's $150,000 Cooperative Computing Award for the first proven 100-million-digit prime.