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

%I A096548 #36 Apr 03 2023 10:36:10
%S A096548 7,289,7,33603,309403,593499
%N A096548 Difference between the smallest 10^n-digit prime and 10^(10^n-1).
%C A096548 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.
%C A096548 a(6) was found by Kenneth Pedersen, Peter Kaiser, and _Patrick De Geest_. - _Charles R Greathouse IV_, Feb 11 2013
%H A096548 Prime Curios, <a href="https://t5k.org/curios/page.php?number_id=3454">10000...33603 (10000-digits).</a>
%H A096548 Chris K. Caldwell, <a href="https://t5k.org/primes/lists/all.txt">The largest known primes.</a>
%H A096548 Chris K. Caldwell, <a href="https://primes.utm.edu/primes/page.php?id=58901">10^999 + 7</a>, related to a(3).
%H A096548 Chris K. Caldwell, <a href="https://primes.utm.edu/primes/page.php?id=66462">10^9999 + 33603</a>, related to a(4).
%H A096548 factordb.com, <a href="http://factordb.com/index.php?id=1000000000022451023">10^999 + 7</a>, contains primality certificate related to a(3).
%H A096548 factordb.com, <a href="http://factordb.com/index.php?id=1100000000081719528">10^9999 + 33603</a>, contains primality certificate related to a(4).
%H A096548 Patrick De Geest, <a href="http://www.worldofnumbers.com/megaprp.htm">10^999999 + y</a>, history of a(6).
%H A096548 Henri Lifchitz, Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/prptop.php">Probable Primes Top 10000.</a>
%H A096548 Henri Lifchitz, Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=10%5E99999%2B309403">10^99999 + 309403</a>, related to a(5).
%H A096548 Henri Lifchitz, Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=10%5E999999%2B593499">10^999999 + 593499</a>, related to a(6).
%H A096548 Hugo Pfoertner, Paul Underwood, Mike Oakes, Daniel Heuer, <a href="/A096548/a096548.txt">Smallest 100000-digit prime?</a>, digest of 7 messages in primeform Yahoo group, Jul 8, 2004. [Cached copy]
%F A096548 a(n) = nextprime(10^(10^n-1)) - 10^(10^n-1) = A007920(10^A002283(n)). - _Jeppe Stig Nielsen_, Jan 23 2021
%e A096548 a(1)=7 because the smallest ten-digit prime is 1000000007.
%e A096548 a(2)=289 because the smallest 100-digit prime is 10^99+289.
%Y A096548 Cf. A033873.
%K A096548 nonn,base,more,hard
%O A096548 1,1
%A A096548 _Hugo Pfoertner_, Jul 06 2004