A118798 Numbers n such that the closest primes surrounding 10^n have the same last two digits.

79, 178, 179, 186, 210, 284, 300, 349, 391, 456, 594, 595, 599, 624, 645, 654, 659, 704, 712, 713, 860, 871, 892, 904, 924, 990, 1015, 1089, 1097, 1110, 1118, 1151, 1165, 1374, 1396, 1459, 1709, 1721, 1826, 1831, 1911, 1943, 1956, 2005, 2061, 2082, 2089

Offset: 1

Author

Cino Hilliard, May 23 2006

Keywords

• easy
• nonn
• base
• less

Comments

79 {251, 49}, 178 {239, 261}, 179 {221, 979}, 186 {479, 721}, 210 {171, 1129}, 284 {467, 133}, 300 {69, 331}, 349 {2603, 297}, 391 {123, 477}, 456 {633, 567}, 594 {11, 789}, 595 {503, 297}, 599 {2339, 2161}, 624 {413, 187}, 645 {3291, 109}, 654 {1811, 1089}, 659 {2363, 937}, 704 {3489, 211},

712 {171, 1029}, 713 {801, 2299}, 860 {1193, 2907}, 871 {827, 1473}, 892 {629, 271}, 904 {503, 597}, 924 {303, 4797}, 990 {3, 1197}, 1015 {71, 1029}, 1089 {4403, 5997}, 1097 {2271, 1429}, 1110 {2373, 2527}, 1118 {1767, 2233}, 1151 {2703, 97}, 1165 {33, 3867}, 1374 {689, 1411},

1396 {1023, 3477}, 1459 {10211, 489}, 1709 {2859, 4241}, 1721 {10311, 189}, 1826 {1761, 1539}, 1831 {17751, 1449}, 1911 {4179, 2621}, 1943 {1279, 1721}, 1956 {541, 9459}, 2005 {141, 14259}, 2061 {6607, 3293}, 2082 {9537, 4563}, 2089 {597, 203}, 2091 {2517, 9783}, 2135 {7287, 3513}, ...,.

Examples

			79 is in the sequence since the two primes nearest primes 10^79 are 10^79 - 251 and 10^79 + 49.
		

Links

• V. Danilov, Smallest and largest n-digit primes.n

Crossrefs

Cf. A115564.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ@k, k-- ]; k]; fQ[n_] := Mod[NextPrim[10^n], 100] == Mod[PrevPrim[10^n], 100]; Do[ If[ fQ@n, Print@n], {n, 2, 1250}] (* Robert G. Wilson v, May 27 2006 *)
Select[Range[2100],Mod[NextPrime[10^#],100]==Mod[NextPrime[10^#,-1],100]&] (* Harvey P. Dale, Mar 09 2019 *)

PARI

g(n) = for(j=1,n,x=precprime(10^j);y=nextprime(10^j);if(x%100==y%100,print1 (j",")))

Formula

A033873 + A033874 == 0 (mod 100). - Robert G. Wilson v, May 27 2006

Extensions

More terms from Robert G. Wilson v, May 27 2006 - Jun 14 2006