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

63, 621, 6101, 11333, 59511, 172473

Offset: 1

Author

Jeppe Stig Nielsen, Jan 26 2021

Keywords

• nonn
• base
• more
• hard

Comments

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.

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A033874, A096548.

Formula

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