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. primesQ5ₚart₁. csv: n = 2 to ~22. 9M (1, 294, 867 primes) primesQ5ₚart₂. csv: n = ~22. 9M to ~47. 9M (1, 294, 868 primes) primesQ5ₚart₃. csv: n = ~47. 9M to ~73. 7M (1, 294, 868 primes) primesQ5ₚart₄. 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
Ruqing Chen (Sun,) studied this question.