Main outstanding problem 

 

Given that the prime values of the quadratic `+`(`*`(27, `*`(`^`(x, 2))), `*`(27, `*`(x)), 7) are precisely those primes p = 1 (mod 3) for which `*`(`^`(factorial(`*`(`+`(p, `-`(1)), `/`(1, 3))), 3)) = 1 (mod p), the nagging question is: what determines the value of factorial(ord[p](`*`(`+`(p, `-`(1)), `/`(1, 3)))) ? 

 

In short, what makes such a prime p be in the (earlier) sequence 

 

3571, 4219, 13669, 25117, 55897, 89269, 102121, 170647,  …            (2) 

 

rather than in the (earlier) sequence
 

7, 61, 331, 547, 1951, 2437, 7351, 8269, 9241, 10267, 23497, …            (4)