A096548 -id:A096548 - cp's OEIS frontend

A212290 Difference between the smallest 10^n-bit prime and 2^(10^n-1).

9, 255, 1239, 5895, 221961

Offset: 1

Charles R Greathouse IV, Jun 16 2012

a(5) found by Serge Batalov, Jun 11 2012.

			2^99+255 is the smallest 100-bit prime, 2^999+1239 is the smallest 1000-bit prime, etc.

Henri Lifchitz, Renaud Lifchitz, Probable Primes Top 10000.

Binary analog of A096548.

PARI
```
a(n)=nextprime(2^(10^n-1))-2^(10^n-1)
```

A340902 Distance from the largest prime with less than 10^n decimal digits to 10^(10^n-1).

Original entry on oeis.org

63, 621, 6101, 11333, 59511, 172473

Offset: 1

Jeppe Stig Nielsen, Jan 26 2021

The prime number related to a(n) is the prime immediately preceding the prime related to A096548(n).

a(5) and a(6) appear to have been first found by Patrick De Geest.

			a(4) = 11333 because 10^9999 - 11333 is the largest prime not exceeding 10^9999.
a(5) = 59511 because 10^99999 - 59511 is the largest prime not exceeding 10^99999.

factordb.com, 10^999 - 6101, contains primality certificate related to a(3).
factordb.com, 10^9999 - 11333, contains primality certificate related to a(4).
Henri Lifchitz, Renaud Lifchitz, 10^99999 - 59511, related to a(5).
Henri Lifchitz, Renaud Lifchitz, 10^999999 - 172473, related to a(6).
Wikipedia, Titanische Primzahl, in German.

Cf. A033874, A096548.

a(n) = 10^(10^n-1) - precprime(10^(10^n-1)) = A064722(10^A002283(n)).

cp's OEIS Frontend

A212290 Difference between the smallest 10^n-bit prime and 2^(10^n-1).

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