Monday, March 16, 2026

Some recent large emirps

In 2007, Jens Kruse Andersen noted the 10007-digit 10^10006+941992101*10^4999+1 as the then-largest-known emirp. Eighteen years later, Stephan Schöler managed to up this by 4 decimal digits with his 3867632931*10^10001+1. In a one-month-ago-today Numberphile, Matt Parker highlighted this discovery, bringing about (of course!) a flurry of new records:

Gamer "Gelly Gelbertson" provided 10^10056+10^6692+10^5872+1, a 10057-digit term in my own OEIS A393530. Mykola Kamenyuk gave us the 11120-digit 117954861*10^11111+1 and (a primo-proof later) 190907571*10^11111+1. More recently, in the YouTube comments, @wuudturner provided the 12346-digit 79191501*10^12338+1 and @vgdominion4049, the 20001-digit 10^20000+518406362*10^9996+1.

I doubt that this is the end of it and I will replace this paragraph with further updates. Email me if you spot any errors or have anything to add.

1 comment:

  1. Well guys, n = 11111 was just a math exercise for me, but now the challenge is accepted!

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