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%I #106 Dec 31 2022 11:50:45
%S 0,17,1060,76127,5736396,454396537,37550402023,3203324994356,
%T 279209790387276,24739512092254535,2220822432581729238,
%U 201467077743744681014,18435588552550705911377,1699246443377779418889494,157589260710736940541561021,14692398516908006398225702366
%N a(n) = sum of primes < 10^n.
%C a(21) was already correctly computed by Marc Deleglise in 2009 but in 2011 he withdrew his result because his verification failed. - _Kim Walisch_, Jun 06 2016
%H Lorenzo Pieri, <a href="/A046731/b046731.txt">Table of n, a(n) for n = 0..26</a> [terms a(0)-a(20) from Marc Deleglise; terms a(21)-a(23) from Kim Walisch; terms a(24)-a(25) from David Baugh]
%H M. Deleglise and J. Rivat, <a href="http://dx.doi.org/10.1090/S0025-5718-96-00674-6">Computing pi(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method</a>, Math. Comp., 65 (1996), 235-245.
%H Cino Hilliard, <a href="https://docs.google.com/document/u/0/d/10raaWNXfi1Xy_RG_1K1_FnE0wBkoT1oYY79dSy_NTnk/pub">GmpDemo Sumprimes</a>.
%H Cino Hilliard, <a href="https://docs.google.com/document/u/0/d/1TbtbUxQyh-oEEN17zJA8pfj6JuGdTlDVDYN9P5-qjqk/pub">Achim Sieve Gmp Sumprimes</a>.
%H Cino Hilliard, <a href="https://docs.google.com/document/u/0/d/1t-4LETx_CBWoObjCIJ21xmY15cQPo6cjN_0rHegclRY/pub">Achim Multi-Prec add Sumprimes</a>.
%H Kim Walisch, <a href="https://github.com/kimwalisch/primesum">primesum program</a>.
%F a(n) is about 100^n/(n log 100). - _Charles R Greathouse IV_, Jan 29 2013
%F a(n) = Sum_{i=2..10^n} A061397(i). - _José de Jesús Camacho Medina_, Aug 08 2016
%e The primes less than 10 give 2+3+5+7 = 17.
%t Join[{0, s = 17}, Table[Do[If[PrimeQ[i], s += i], {i, 10^n + 1, 10^(n + 1), 2}]; s, {n, 7}]] (* _Jayanta Basu_, Jun 28 2013 *)
%t Table[Sum[Prime[i], {i, PrimePi[10^n]}], {n, 0, 7}] (* _Kim Walisch_, Dec 21 2017 *)
%o (PARI) a(n) = my(s=0); forprime(p=1, 10^n, s += p); s; \\ _Michel Marcus_, Jan 14 2015
%o (Perl) use ntheory ":all"; say "$_ ",sum_primes(10**$_) for 0..15; # _Dana Jacobsen_, May 04 2017
%Y Cf. A034387.
%K nonn,nice
%O 0,2
%A _Enoch Haga_
%E Corrected and extended by _Jud McCranie_
%E a(12) and a(13) from _Cino Hilliard_, Aug 14 2006
%E New value for a(13) from _Cino Hilliard_, Oct 24 2007
%E There was indeed an error in a(13) both in the entry here and in the b-file. This has now been corrected. - _N. J. A. Sloane_, Nov 23 2007
%E Two new values from _Marc Deleglise_, May 21 2008 - see the b-file.
%E a(21) from _Marc Deleglise_, Jun 29 2008 - see the b-file.
%E Nov 15 2011: _Marc Deleglise_ has withdrawn his value for a(21).
%E a(21)-a(22) from _Kim Walisch_, Jun 06 2016
%E a(23) from _Kim Walisch_, Jun 11 2016
%E a(24) from _David Baugh_ using Kim Walisch's primesum program, Jun 17 2016
%E a(25) from _David Baugh_ using Kim Walisch's primesum program, Oct 16 2016
%E a(26) from _Kim Walisch_, May 25 2022, added by _Lorenzo Pieri_
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