A084413 -id:A084413 - cp's OEIS frontend

A069691 Smallest prime with internal digits = n; or 0 if no such number exists.

101, 113, 127, 131, 149, 151, 163, 173, 181, 191, 1103, 1117, 1123, 2131, 2141, 1151, 1163, 1171, 1181, 1193, 1201, 1213, 1223, 1231, 1249, 1259, 2267, 1277, 1283, 1291, 1301, 1319, 1321, 2333, 2341, 2351, 1361, 1373, 1381, 1399, 1409, 2411, 1423, 1433, 1447

Offset: 0

Amarnath Murthy, Apr 06 2002

By placing one digit on both sides of n one get 36 different numbers that might be primes ( 1 to 9 on left and 1,3,7,9 on right). If none of these numbers is a prime then a(n) = 0.

The smallest value of n for which a(n) = 0 is 2437 = A032734(0). - Rick L. Shepherd and Reinhard Zumkeller, Jul 17 2002

			a(25) = 1259 is prime with internal digits =25.

Robert Price, Table of n, a(n) for n = 0..10000
Index entries for primes involving decimal expansion of n

Cf. A032734, A030665, A069691, A077501, A084413.

Corrected and extended by Larry Reeves, Rick L. Shepherd and Reinhard Zumkeller, Jul 17 2002

A038370 Smallest prime with "n^2" as central digit(s).

Original entry on oeis.org

101, 113, 149, 191, 1163, 1259, 1361, 1493, 2647, 1811, 11003, 11213, 11443, 11699, 11969, 12251, 12569, 12893, 13241, 13613, 14009, 14411, 14843, 15299, 15761, 16253, 16763, 17291, 27847, 18413, 19001, 29611, 210241, 110899, 311561, 112253, 112967

Offset: 0

Zak Seidov, Jun 25 2003

1195 is the smallest n such that 2 digits are needed on both sides of 1195^2 = 1428025 to give prime 10142802503. - Michel Marcus, Jun 05 2013

Cf. A084413, A069691.

a(n) = {a = 1; ok = 0; while (!ok, lena = #Str(a); lenn = #Str(n^2); for (b=0, 10^lena - 1, p = b + 10^lena*n^2 + 10^(lenn+lena)*a; if (isprime(p), return (p)););a++;);} \\ Michel Marcus, Jun 05 2013

Corrected by Robert G. Wilson v, Jun 27 2003

a(19) corrected by Sean A. Irvine, Jan 12 2021

A084430 Smallest prime with "n^3" as central digit(s).

Original entry on oeis.org

101, 113, 181, 1277, 2647, 11251, 12161, 23431, 15121, 17291, 410009, 213319, 117281, 421973, 127447, 233759, 240967, 249131, 158329, 168599, 180001, 192611, 1106489, 1121671, 2138249, 2156251, 1175767, 1196837, 2219527, 2243893, 1270001, 3297911, 2327681

Offset: 0

Zak Seidov, Jun 27 2003

Cf. A038370, A084413, A069691.

a(n) = {n = n^3; for (i = 1, 9, forstep (j=1, 9, 2, v = j + 10*n + i*10^(1+length(Str(n))); if (isprime(v), return (v)); ); ); } \\ Michel Marcus, Oct 05 2013

More terms from Michel Marcus, Oct 05 2013

cp's OEIS Frontend

A069691 Smallest prime with internal digits = n; or 0 if no such number exists.

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A038370 Smallest prime with "n^2" as central digit(s).

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A084430 Smallest prime with "n^3" as central digit(s).

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