cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A160022 Primes p such that p^4 + 5^4 + 3^4 is prime.

Original entry on oeis.org

3, 23, 47, 53, 67, 73, 89, 101, 103, 109, 151, 157, 179, 229, 521, 557, 569, 619, 661, 821, 977, 1013, 1087, 1129, 1277, 1321, 1451, 1559, 1607, 1627, 1741, 1867, 1871, 1949, 2137, 2389, 2441, 2797, 3271, 3313, 3643, 3677, 3769, 3847, 4001, 4027, 4133
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Keywords

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 5, r = 3.
It is conjectured that the sequence is infinite.
There are twin prime (101, 103) and other consecutive primes (151, 157; 1867, 1871) in the sequence.

Examples

			p = 3: 3^4 + 5^4 + 3^4 = 787 is prime, so 3 is in the sequence.
p = 5: 5^4 + 5^4 + 3^4 = 1331 = 11^3, so 5 is not in the sequence.
p = 101: 101^4 + 5^4 + 3^4 = 104061107 is prime, so 101 is in the sequence.
p = 103: 103^4 + 5^4 + 3^4 = 112551587 is prime, so 103 is in the sequence.

Crossrefs

Cf. A158979, A159829, A160031.

Programs

  • Magma
    [p: p in PrimesUpTo(5000)|IsPrime(p^4+706)] // Vincenzo Librandi, Dec 18 2010
  • Mathematica
    With[{c=5^4+3^4},Select[Prime[Range[600]],PrimeQ[#^4+c]&]] (* Harvey P. Dale, Aug 14 2011 *)
  • PARI
    is(n)=isprime(n) && isprime(n^4+706) \\ Charles R Greathouse IV, Jun 07 2016

Extensions

Edited, 1607 inserted and extended beyond 3643 by Klaus Brockhaus, May 03 2009

A160031 Primes p such that p^4 + 2*3^4 is prime.

Original entry on oeis.org

5, 13, 19, 43, 71, 83, 97, 101, 107, 109, 127, 149, 179, 193, 197, 211, 233, 241, 311, 353, 383, 401, 421, 541, 577, 599, 607, 619, 641, 647, 683, 709, 727, 751, 769, 827, 877, 883, 941, 967, 991, 1009, 1061, 1097, 1109, 1187, 1289, 1373, 1381, 1409, 1439
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Keywords

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (107, 109) and other consecutive primes (193, 197) in the sequence.

Examples

			p = 5: 5^4 + 2*3^4 = 787 is prime, so 5 is in the sequence.
p = 7: 7^4 + 2*3^4 = 2563 = 11*233, so 7 is not in the sequence.
p = 107: 107^4 + 2*3^4 = 131079763 is prime, so 107 is in the sequence.
p = 109: 109^4 + 2*3^4 = 141158323 is prime, so 109 is in the sequence.

Links

Crossrefs

Cf. A158979, A159829, A160022.

Programs

Extensions

Edited and extended beyond 683 by Klaus Brockhaus, May 03 2009

A160023 Primes p such that p^4 + 7^4 + 3^4 is prime.

Original entry on oeis.org

11, 37, 71, 101, 149, 163, 191, 271, 293, 379, 409, 419, 647, 661, 709, 1153, 1193, 1231, 1277, 1523, 1583, 1619, 1667, 1693, 1753, 1777, 1787, 1913, 2089, 2099, 2161, 2213, 2441, 2473, 2531, 2551, 2609, 2711, 2749, 2909, 2953, 2999, 3221, 3257, 3469
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Keywords

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 7, r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (6197, 6199) and other consecutive primes (409, 419; 2089, 2099) in the sequence.

Examples

			p = 7: 7^4 + 7^4 + 3^4 = 4883 = 19*257, so 7 is not in the sequence.
p = 11: 11^4 + 7^4 + 3^4 = 17123 is prime, so 11 is in the sequence.
p = 101: 101^4 + 7^4 + 3^4 = 104062883 is prime, so 101 is in the sequence.

Links

Crossrefs

Cf. A158979, A159829, A160022.

Programs

  • Magma
    [ p: p in PrimesUpTo(3500) | IsPrime(p^4+2482) ]; // Klaus Brockhaus, May 03 2009
  • Mathematica
    Select[Prime[Range[500]],PrimeQ[#^4+2482]&] (* Harvey P. Dale, Jan 31 2017 *)

Extensions

Edited and extended beyond 2441 by Klaus Brockhaus, May 03 2009

A160024 Primes p such that p^4 + 11^4 + 3^4 is prime.

Original entry on oeis.org

7, 11, 13, 19, 23, 31, 41, 47, 61, 67, 73, 83, 101, 107, 127, 157, 163, 191, 193, 277, 281, 311, 337, 373, 379, 401, 409, 431, 443, 461, 491, 523, 541, 569, 607, 643, 673, 691, 719, 733, 743, 757, 769, 887, 929, 947, 953, 1031, 1039, 1087, 1093, 1097, 1103, 1109
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Keywords

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 11, r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (11, 13) and other consecutive primes (7, 11; 1093, 1097) in the sequence.

Examples

			p = 3: 3^4 + 11^4 + 3^4 = 14803 = 113*131, so 3 is not in the sequence.
p = 7: 7^4 + 11^4 + 3^4 = 17123 is prime, so 7 is in the sequence.
p = 11: 11^4 + 11^4 + 3^4 = 29363 is prime, so 11 is in the sequence.
p = 13: 13^4 + 11^4 + 3^4 = 43283 is prime, so 13 is in the sequence.

Links

Crossrefs

Cf. A158979, A159829, A160022.

Programs

  • Magma
    [ p: p in PrimesUpTo(1110) | IsPrime(p^4+14722) ]; // Klaus Brockhaus, May 03 2009
  • Mathematica
    Select[Prime[Range[200]],PrimeQ[#^4+14722]&] (* Harvey P. Dale, Apr 18 2023 *)

Extensions

Edited and extended beyond 461 by Klaus Brockhaus, May 03 2009

A160025 Primes p such that p^4 + 13^4 + 3^4 is prime.

Original entry on oeis.org

3, 11, 13, 17, 31, 41, 43, 53, 83, 127, 167, 181, 193, 211, 241, 311, 337, 349, 421, 431, 487, 521, 557, 613, 617, 647, 701, 769, 811, 857, 953, 1021, 1151, 1249, 1289, 1303, 1373, 1453, 1459, 1471, 1523, 1553, 1567, 1579, 1613, 1663, 1669, 1747, 1823, 1831
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Keywords

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 13, r = 3.
It is conjectured that the sequence is infinite.
There are prime twins (11, 13) and other consecutive primes (421, 431; 1823, 1831) in the sequence.

Examples

			p = 3: 3^4 + 13^4 + 3^4 = 28723 is prime, so 3 is in the sequence.
p = 5: 5^4 + 13^4 + 3^4 = 29267 = 7*37*113, so 5 is not in the sequence.
p = 17: 17^4 + 13^4 + 3^4 = 112163 is prime, so 17 is in the sequence.
p = 83: 83^4 + 13^4 + 3^4 = 47486963 is prime, so 83 is in the sequence.

Links

Crossrefs

Cf. A158979, A159829, A160022.

Programs

  • Magma
    [ p: p in PrimesUpTo(1840) | IsPrime(p^4+28642) ]; // Klaus Brockhaus, May 03 2009
  • Mathematica
    Select[Prime[Range[400]],PrimeQ[#^4+28642]&] (* Harvey P. Dale, Dec 14 2011 *)

Extensions

Edited and extended beyond 857 by Klaus Brockhaus, May 03 2009

A160026 Primes p such that p^4 + 17^4 + 3^4 is prime.

Original entry on oeis.org

13, 29, 37, 59, 89, 101, 107, 241, 263, 293, 373, 409, 569, 683, 821, 971, 1033, 1187, 1229, 1277, 1289, 1423, 1511, 1627, 1759, 1823, 1901, 1907, 1973, 2011, 2069, 2083, 2099, 2207, 2311, 2473, 2593, 2633, 2707, 2719, 2753, 2819, 3023, 3137, 3209, 3221
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

Keywords

Comments

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 17, r = 3.
It is conjectured that the sequence is infinite.
There are consecutive primes (1901, 1907) in the sequence.

Examples

			p = 3: 3^4 + 17^4 + 3^4 = 83683 = 67*1249, so 3 is not in the sequence.
p = 1901: 1901^4 + 17^4 + 3^4 = 13059557751203 is prime, so 1901 is in the sequence.
p = 1907: 1907^4 + 17^4 + 3^4 = 13225216032803 is prime, so 1907 is in the sequence.

Crossrefs

Cf. A158979, A159829, A160022.

Programs

  • Magma
    [ p: p in PrimesUpTo(3250) | IsPrime(p^4+83602) ]; // Klaus Brockhaus, May 03 2009

Extensions

Edited, 409 inserted and extended beyond 2069 by Klaus Brockhaus, May 03 2009
Showing 1-6 of 6 results.

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