A033874 -id:A033874 - cp's OEIS frontend

A185201 10^n - second largest prime less than 10^n.

5, 11, 9, 33, 11, 21, 27, 29, 71, 57, 53, 39, 137, 29, 53, 83, 23, 33, 57, 27, 113, 71, 53, 303, 321, 249, 107, 261, 53, 17, 81, 119, 47, 513, 237, 179, 123, 123, 173, 27, 203, 137, 119, 77, 119, 147, 83, 47, 183, 161, 333, 339, 611, 579

Offset: 1

Washington Bomfim, Jan 24 2012

nonn

			a(1) = 5 because precprime(10) = 7, and precprime(6) = 5.
From _M. F. Hasler_, Jul 19 2024: (Start)
Further examples: (where pp = prevprime = A151799)
    n |   pp(pp(10^n))  | a(n)
  ----+-----------------+------
    1 |               5 |   5
    2 |              89 |  11
    3 |             991 |   9
    4 |            9967 |  33
    5 |           99989 |  11
    6 |          999979 |  21
    7 |         9999973 |  27
    8 |        99999971 |  29
    9 |       999999929 |  71
   10 |      9999999943 |  57
   11 |     99999999947 |  53
   12 |    999999999961 |  39
   13 |   9999999999863 | 137
   14 |  99999999999971 |  29
   15 | 999999999999947 |  53
(End)

D. E. Knuth, The Art of Computer Programming, Second Edition, Vol. 2, Seminumerical Algorithms, Chapter 4.5.4 Factoring into Primes, Table 1, Page 390, Addison-Wesley, Reading, MA, 1981.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A033874.

Cf. A003618 (largest prime < 10^n), A151799 (prevprime function).

seq(10^n - prevprime(prevprime(10^n)),n=1..100); # Robert Israel, May 28 2017

Table[10^n - NextPrime[10^n, -2], {n,1,50}] (* G. C. Greubel, Jun 24 2017 *)

apply( {A185201(n)=10^n-precprime(precprime(10^n)-1)}, [1..66]) \\ M. F. Hasler, Jul 19 2024

a(n) = 10^n - precprime(precprime(10^n)-1)

A097519 Prime differences between nextprime(2^n) and 2^n.

Original entry on oeis.org

3, 5, 3, 3, 7, 5, 3, 17, 3, 29, 3, 7, 17, 43, 29, 3, 11, 3, 11, 17, 53, 31, 7, 23, 29, 7, 59, 5, 5, 3, 131, 29, 13, 131, 3, 29, 11, 29, 37, 11, 7, 23, 13, 17, 3, 7, 29, 59, 61, 7, 277, 281, 43, 71, 29, 41, 277, 67, 7, 29, 17, 67, 37, 5, 5, 97, 7, 107, 19, 83, 7, 5, 107, 101

Offset: 1

Cino Hilliard, Aug 27 2004

nonn

Primes in A013597. - Bill McEachen, Oct 27 2021

Cf. A033873, A033874, A013597.

Select[Table[NextPrime[2^n]-2^n, {n,200}], PrimeQ] (* Harvey P. Dale, Dec 13 2011 *)
Select[NextPrime[#]-#&/@(2^Range[200]),PrimeQ] (* Harvey P. Dale, Jan 05 2024 *)

Definition corrected by Harvey P. Dale, Dec 13 2011

A120099 Numbers n such that the closest primes surrounding 10^n are the same distance modulo 100.

Original entry on oeis.org

17, 45, 87, 101, 112, 230, 270, 341, 468, 472, 473, 479, 517, 554, 555, 568, 650, 657, 663, 696, 718, 727, 810, 830, 836, 900, 917, 952, 984, 988, 1020, 1021, 1022, 1059, 1140, 1142, 1167, 1200, 1295, 1326, 1400, 1401, 1405, 1406, 1418, 1449, 1499, 1503, 1526

Offset: 1

Cino Hilliard and Robert G. Wilson v, Jun 08 2006

{3, 3}, 45 {9, 9}, 87 {373, 273}, 101 {3, 203}, 112 {207, 807}, 230 {753, 1053}, 270 {361, 861}, 341 {831, 1331}, 468 {301, 801}, 472 {1569, 2669}, 473 {99, 599}, 479 {109, 209}, 554 {937, 437}, 555 {151, 2151}, 568 {501, 801}, 650 {1999, 899}, 657 {1791, 291}, 663 {6333, 33},
{61, 1361}, 718 {5863, 1463}, 727 {273, 1073}, 810 {1591, 2891}, 830 {2853, 1253}, 836 {2809, 1209}, 900 {1873, 773}, 917 {693, 5393}, 952 {4827, 27}, 984 {1867, 2867}, 988 {753, 1053}, 1020 {793, 1193}, 1021 {1609, 6209}, 1022 {853, 1053} 1059 {5793, 1293}, 1140 {357, 4857},
{4329, 5829}, 1167 {1131, 3231}, 1200 {5227, 4127}, 1295 {5169, 2369}, 1326 {907, 4007}, 1400 {13317, 2517}, 1401 {10549, 2249}, 1405 {4329, 629}, 1406 {7477, 10277}, 1418 {841, 8741}, 1449 {2989, 3089}, 1499 {2001, 1901}, 1503 {439, 339}, 1526 {4603, 603}, 1534 {2409, 3209}, ...,.

Cf. A115564, A118798.

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ ! PrimeQ@k, k-- ]; k]; Do[ If[ Mod[ NextPrim[10^n], 100] == Mod[10^n - PrevPrim[10^n], 100], Print[{n, a, b}]], {n, 1320}]
Select[Range[1530],Mod[NextPrime[10^#]-10^#,100]==Mod[10^# -NextPrime[ 10^#,-1],100]&] (* Harvey P. Dale, Sep 24 2021 *)

A033873 (mod 100) == A033874 (mod 100).

More terms from Robert G. Wilson v, Jun 09 2006

Corrected (term 517 added) by Harvey P. Dale, Sep 25 2021

A340902 Distance from the largest prime with less than 10^n decimal digits to 10^(10^n-1).

Original entry on oeis.org

63, 621, 6101, 11333, 59511, 172473

Offset: 1

Jeppe Stig Nielsen, Jan 26 2021

The prime number related to a(n) is the prime immediately preceding the prime related to A096548(n).

a(5) and a(6) appear to have been first found by Patrick De Geest.

			a(4) = 11333 because 10^9999 - 11333 is the largest prime not exceeding 10^9999.
a(5) = 59511 because 10^99999 - 59511 is the largest prime not exceeding 10^99999.

factordb.com, 10^999 - 6101, contains primality certificate related to a(3).
factordb.com, 10^9999 - 11333, contains primality certificate related to a(4).
Henri Lifchitz, Renaud Lifchitz, 10^99999 - 59511, related to a(5).
Henri Lifchitz, Renaud Lifchitz, 10^999999 - 172473, related to a(6).
Wikipedia, Titanische Primzahl, in German.

Cf. A033874, A096548.

a(n) = 10^(10^n-1) - precprime(10^(10^n-1)) = A064722(10^A002283(n)).

cp's OEIS Frontend

A185201 10^n - second largest prime less than 10^n.

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A097519 Prime differences between nextprime(2^n) and 2^n.

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A120099 Numbers n such that the closest primes surrounding 10^n are the same distance modulo 100.

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Mathematica

Formula

Extensions

A340902 Distance from the largest prime with less than 10^n decimal digits to 10^(10^n-1).

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