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+ digit-lengths. I was going to attempt a search for a record large pair but gamer "Gelly Gelbertson" beat me to it with his Numberphile video comment (10^10056+10^4184+10^3364+1, 10^10056+10^6692+10^5872+1), apparently made on February 18th (although I discovered it only on March 14th):
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| click to enlarge |
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