A124013
Lesser of pair of most widely separated primes whose sum is 10^n.
Original entry on oeis.org
3, 3, 3, 59, 11, 17, 29, 11, 71, 71, 23, 11, 29, 29, 11, 83, 3, 11, 281, 11, 101, 71, 23, 257, 401, 293, 107, 293, 53, 11, 113, 251, 47, 587, 23, 179, 389, 59, 173, 17, 1427, 83, 431, 53, 563, 593, 41, 47, 239, 383, 431, 1181, 701, 971, 149, 593, 569, 149, 191, 1973
Offset: 1
10^1 = 3 + 7, 10^2 = 3 + 97, 10^3 = 3 + 997, 10^4 = 59 + 9941, 10^5 = 11 + 99989, 10^6 = 17 + 999983, 10^7 = 29 + 9999971, 10^8 = 11 + 99999989, 10^9 = 71 + 999999929, 10^10 = 71 + 9999999929, etc.
Cf.
A065577 (Number of Goldbach partitions of 10^n),
A124450 (Lesser of pair of closest primes summed to 10^n).
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Table[DeleteCases[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]] /. {, k} /; ! PrimeQ@ k -> 0, 0][[1, 1]], {n, 8}] (* or *)
Table[First@ SelectFirst[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]], PrimeQ@ Last@ # &], {n, 9}] (* Version 10, Michael De Vlieger, Aug 01 2016 *)
lp[n_]:=Module[{p=3,x=10^n},While[CompositeQ[x-p],p=NextPrime[p]];p]; Array[lp,60] (* Harvey P. Dale, Jun 11 2022 *)
a(1) corrected and a(2) inserted by
Gionata Neri, Aug 01 2016
A124049
a(n) = c is least number such that 10^n/2 -/+ c are primes.
Original entry on oeis.org
0, 3, 9, 81, 123, 57, 87, 243, 69, 63, 189, 231, 1569, 381, 231, 1443, 1113, 321, 339, 1353, 363, 519, 1323, 1503, 741, 1221, 957, 1053, 339, 5931, 2121, 2301, 2031, 4773, 4737, 10281, 1317, 129, 3873, 1443, 387, 11769, 8271, 5337, 2883, 7137, 8193, 8493
Offset: 1
Next terms up to n = 101: 14637, 9897,
6471, 183, 8043, 6921,6699, 29127, 3663, 12537, 3777,
6741, 2253, 561, 3783, 26979, 16491, 6543, 10683,
1749, 6417, 38871, 22767, 62403, 8631, 4497, 20739,
453, 16731, 25293, 4341, 37467,
55323,4587,37083,24717,6687,8763,22551,29367,37881,14301,8637,34101,22179,26811,7059,1647
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lnc[n_]:=Module[{c=0,t=10^n/2},While[!AllTrue[t+{c,-c},PrimeQ],c++];c]; Array[ lnc,50] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 21 2014 *)
A137611
Lesser of a pair of distinct closest n-digit primes that add up to 10^n.
Original entry on oeis.org
3, 47, 491, 4919, 49877, 499943, 4999913, 49999757, 499999931, 4999999937, 49999999811, 499999999769, 4999999998431, 49999999999619, 499999999999769, 4999999999998557, 49999999999998887, 499999999999999679
Offset: 1
Apart from initial term, same as
A124450.
A-number in cross-reference corrected by
R. J. Mathar, Jul 17 2009
A135057
Largest semiprime whose prime factors add up to 10^n.
Original entry on oeis.org
25, 2491, 249919, 24993439, 2499984871, 249999996751, 24999999992431, 2499999999940951, 249999999999995239, 24999999999999996031, 2499999999999999964279, 249999999999999999946639, 24999999999999999997538239, 2499999999999999999999854839, 249999999999999999999999946639
Offset: 1
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s={};f[{p_,e_}]:=e*p;Do[a=(10^n/2)^2;While[PrimeOmega[a]!=2||Total[f/@FactorInteger[a]]!=10^n,a=a-1];AppendTo[s,a],{n,11}];s (* James C. McMahon, Apr 13 2025 *)
Showing 1-4 of 4 results.
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