After watching Matt Parker's February 16th Numberphile video on Stephan Schöler's largest currently known emirp, I wondered of course if any of the primes that are the sum of four distinct powers of ten (A157711, on which I have been working now for nine months) were emirps. It turns out there were a healthy number and I decided to create two new OEIS sequences for them: A393530 and A393531.
While more than half (533) of the first 1000 digit-lengths had no solutions, the others had anywhere from 1 to 7 (digit-length 41) solutions. Moreover, the accumulation of emirp-pair counts showed a steady rise, giving me hope that this would continue for larger digit-lengths:
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| emirp-pair count accumulations for the first 1036 digit-lengths (click to enlarge) |
I will see if I can increase my counts to 2000+. This will take some weeks. At the same time I'll try a limited sampling of solution searches for digit-lengths greater than 10011 to see if I can luck into a record large emirp.
