A096548 Difference between the smallest 10^n-digit prime and 10^(10^n-1).

7, 289, 7, 33603, 309403, 593499

Offset: 1

Author

Hugo Pfoertner, Jul 06 2004

Keywords

• nonn
• base
• more
• hard

Comments

Daniel Heuer found a(5) in 2004 by sieving up to 2^33 and then checking ~8000 candidates with pfgw-linux. Proving primality of 10^99999+309403 is beyond current (2004) technology.

a(6) was found by Kenneth Pedersen, Peter Kaiser, and Patrick De Geest. - Charles R Greathouse IV, Feb 11 2013

Examples

			a(1)=7 because the smallest ten-digit prime is 1000000007.
a(2)=289 because the smallest 100-digit prime is 10^99+289.
		

Links

• Prime Curios, 10000...33603 (10000-digits).
• Chris K. Caldwell, The largest known primes.
• Chris K. Caldwell, 10^999 + 7, related to a(3).
• Chris K. Caldwell, 10^9999 + 33603, related to a(4).
• factordb.com, 10^999 + 7, contains primality certificate related to a(3).
• factordb.com, 10^9999 + 33603, contains primality certificate related to a(4).
• Patrick De Geest, 10^999999 + y, history of a(6).
• Henri Lifchitz, Renaud Lifchitz, Probable Primes Top 10000.
• Henri Lifchitz, Renaud Lifchitz, 10^99999 + 309403, related to a(5).
• Henri Lifchitz, Renaud Lifchitz, 10^999999 + 593499, related to a(6).
• Hugo Pfoertner, Paul Underwood, Mike Oakes, Daniel Heuer, Smallest 100000-digit prime?, digest of 7 messages in primeform Yahoo group, Jul 8, 2004. [Cached copy]

Crossrefs

Cf. A033873.

Formula

a(n) = nextprime(10^(10^n-1)) - 10^(10^n-1) = A007920(10^A002283(n)). - Jeppe Stig Nielsen, Jan 23 2021