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%I #38 Jul 11 2023 19:30:48
%S 17,1043,75067,5660269,448660141,37096005486,3165774592333,
%T 276006465392920,24460302301867259,2196082920489474703,
%U 199246255311162951776,18234121474806961230363,1680810854825228712978117,155890014267359161122671527,14534809256197269457684141345,1361418455796443892761407164186
%N Sum of all primes having n decimal digits.
%C Also the sum of the primes between 10^(n-1) and 10^n.
%C a(12) to a(20) were computed from A046731(12)-A046731(11) to A046731(20)-A046731(19). - _Cino Hilliard_, May 31 2008
%C A good estimate for the sum of the primes < k is k^2/(2*log(k)-1). Using this formula, a(20)~(10^20)^2/(2*log(10^20)-1) -(10^19)^2/(2*log(10^19)-1) = 108609290005707493265628731014013409909. The relative error this formula produces for the last 5 terms is a(16): -0.00019454, a(17): -0.00017176, a(18): -0.00015275, a(19): -0.00013674, a(20): -0.00012312. - _Cino Hilliard_, May 31 2008
%H Hugo Pfoertner, <a href="/A077645/b077645.txt">Table of n, a(n) for n = 1..26</a> (terms 1..20 from Cino Hilliard).
%H Cino Hilliard, <a href="http://docs.google.com/Doc?id=dgpq9w4b_11m7tc9r">Count,Sum primes in a range Win32 Gcc+Gmp</a>.
%F a(n) = Sum_{10^(n-1) <= p <= 10^n, p prime} p = A007504(A000720(10^n)) - A007504(A000720(10^(n-1))).
%e a(1) = 2 + 3 + 5 + 7 = 17, sum of four 1-digit primes.
%p a:=proc(n) local tot,b,j: tot:=nextprime(10^(n-1)): b:=nextprime(10^(n-1)): for j while nextprime(b) < 10^n do tot:=tot+nextprime(b): b:=nextprime(b) end do:tot end proc: # _Emeric Deutsch_, Oct 08 2007
%t Prepend[Table[Apply[Plus,Table[Prime[w],{w,PrimePi[10^(n-1)]+1,PrimePi[10^n]}]],{n,2,7}],17] (* corrected by _Ivan N. Ianakiev_, Aug 12 2016 *)
%Y Cf. A000040, A000720, A006879, A007504.
%K base,nonn
%O 1,1
%A _Labos Elemer_, Nov 18 2002
%E 2 more terms from _Lior Manor_, Sep 11 2007
%E Corrected and extended by _Emeric Deutsch_, Oct 08 2007
%E More terms from _Cino Hilliard_, May 31 2008
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