Prime values and consecutive-prime clusters of n⁵ − (n−1)⁵: Computation, heuristics, and large probable prime generation

Exhaustive enumeration of all 5,179,467 positive integers n ≤ 10⁸ for which Q(n) = n⁵ − (n−1)⁵ is prime, together with large probable prime (PRP) data and an ECPP primality certificate. Prime tables (4 CSV files): Each file contains two columns (n, Q(n)) with a header row. The four parts collectively cover n = 2 to 99,999,997 and contain all primes of the form Q(n) in this range. primes_Q5_part_1.csv: n = 2 to ~22.9M (1,294,867 primes) primes_Q5_part_2.csv: n = ~22.9M to ~47.9M (1,294,868 primes) primes_Q5_part_3.csv: n = ~47.9M to ~73.7M (1,294,868 primes) primes_Q5_part_4.csv: n = ~73.7M to 10⁸ (1,294,867 primes) PRP and ECPP data: 175 probable primes with ~10,000 digits (base 10²⁴⁹⁹) 2 probable primes with ~50,000 digits (base 10¹²⁴⁹⁹) 1 probable prime with ~100,000 digits (base 10²⁴⁹⁹⁹) 1 probable prime with ~200,000 digits (base 10⁴⁹⁹⁹⁹) ECPP certificate (Primo 4.3.3) proving Q(10²⁴⁹⁹ + 3469) is a 9,997-digit prime Tuplet data: All 458 quintuplets and 25 sextuplets for n ≤ 1.9 × 10⁹ For methodology, analysis, and source code, see the accompanying paper and GitHub repository: https://github.com/GUTgeoservice/Q5-primes