A168375 -id:A168375 - cp's OEIS frontend

A168417 Primes q for which 1 concatenated with q^3 (A168327) is prime.

3, 13, 103, 109, 139, 163, 181, 211, 379, 457, 463, 1021, 1087, 1123, 1201, 1249, 1303, 1381, 1579, 1597, 1609, 1699, 1861, 1873, 1987, 2011, 2029, 2053, 2143, 2221, 2281, 2341, 2473, 2503, 2557, 2731, 2857, 3061, 3067, 3217, 3253, 3271, 3319, 3331, 3517

Offset: 1

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 25 2009

It is conjectured that this sequence is infinite.

			(1) "1 3^3"=10^2+3^3=127=prime(31) gives a(1)=3=prime(2)
(2) "1 103^3"=10^7+103^3=11092727=prime(732258) gives a(3)=103=prime(27)

Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
A168327 Primes of concatenated form p= "1 n^3"
A168375 Natural numbers n for which the concatenation p= "1 n^3" is prime

Select[Prime[Range[500]],PrimeQ[FromDigits[Join[{1},IntegerDigits[ #^3]]]]&] (* Harvey P. Dale, Jan 21 2013 *)

Edited and extended by Charles R Greathouse IV, Apr 23 2010

A168540 Natural numbers n for which 100n^3 + 27 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 13, 17, 25, 29, 32, 44, 55, 61, 76, 77, 80, 92, 106, 109, 112, 116, 121, 124, 136, 137, 142, 143, 149, 152, 154, 158, 161, 169, 170, 178, 190, 191, 196, 200, 208, 221, 223, 224, 227, 230, 245, 254, 259, 260, 262

Offset: 1

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 29 2009

nonn

It is conjectured that sequence is infinite.

			(1) 3^3+10^2*1^3=127=prime(31) gives a(1)=1
(2) 3^3+10^2*2^3=827=prime(144) gives a(2)=2
(3) 3^3+10^2*13^3=219727=prime(19588) gives a(6)=13

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

Cf. A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
Cf. A168327 Primes of concatenated form p= "1 n^3"
Cf. A168375 Natural numbers n for which the concatenation p= "1 n^3"is prime

Select[Range[300],PrimeQ[100#^3+27]&] (* Harvey P. Dale, May 10 2013 *)

Edited by Charles R Greathouse IV, Apr 28 2010

A169586 Primes p in A168540 for which q = 3^3 + 10^2*p^3 (A168487) is prime.

Original entry on oeis.org

2, 5, 7, 13, 17, 29, 61, 109, 137, 149, 191, 223, 227, 269, 311, 331, 337, 359, 389, 397, 409, 433, 457, 467, 491, 587, 619, 653, 661, 709, 727

Offset: 1

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 02 2009

nonn

It is conjectured that sequence is infinite

			(1) 3^3+10^2*2^3=827=prime(144) gives a(1)=2=prime(1)
(2) 3^3+10^2*5^3=12527=prime(1496) gives a(2)=5=prime(3)
(3) 3^3+10^2*13^3=219727=prime(19588) gives a(4)=13=prime(6)

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005
Arnold Scholz, Bruno Schoeneberg: Einführung in die Zahlentheorie, Walter de Gruyter, 5. Auflage 1973

A000040 The prime numbers
A167535 Concatenation of two square numbers which give a prime
A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
A168327 Primes of concatenated form p= "1 n^3"
A168375 Naturals n for which the concatenation p= "1 n^3"is prime
A168487 Primes of form p = 3^3 + 10^2*n^3 with a natural number n
A168540 Naturals n for which the concatenation p = 3^3 + 10^2*n^3 is prime

cp's OEIS Frontend

A168417 Primes q for which 1 concatenated with q^3 (A168327) is prime.

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A168540 Natural numbers n for which 100n^3 + 27 is prime.

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A169586 Primes p in A168540 for which q = 3^3 + 10^2*p^3 (A168487) is prime.

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