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 A096548 Difference between the smallest 10^n-digit prime and 10^(10^n-1). 3
 7, 289, 7, 33603, 309403, 593499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Table of n, a(n) for n=1..6. 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] FORMULA a(n) = nextprime(10^(10^n-1)) - 10^(10^n-1) = A007920(10^A002283(n)). - Jeppe Stig Nielsen, Jan 23 2021 EXAMPLE a(1)=7 because the smallest ten-digit prime is 1000000007. a(2)=289 because the smallest 100-digit prime is 10^99+289. CROSSREFS Cf. A033873. Sequence in context: A009503 A209889 A176072 * A160072 A137435 A220241 Adjacent sequences: A096545 A096546 A096547 * A096549 A096550 A096551 KEYWORD nonn,base,more,hard AUTHOR Hugo Pfoertner, Jul 06 2004 STATUS approved

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Last modified February 22 16:01 EST 2024. Contains 370256 sequences. (Running on oeis4.)