A107132 -id:A107132 - cp's OEIS frontend

A107158 Primes of the form 3x^2 + 17y^2.

3, 17, 29, 71, 311, 317, 347, 419, 431, 449, 617, 743, 857, 881, 941, 947, 1013, 1091, 1151, 1163, 1193, 1217, 1451, 1601, 1847, 1877, 2063, 2069, 2153, 2207, 2357, 2411, 2459, 2591, 2777, 2861, 2963, 3023, 3089, 3257, 3359, 3407, 3461, 3533

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -204. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[3, 0, 17, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\17), if(isprime(t=w+17*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107160 Primes of the form x^2 + 52y^2.

Original entry on oeis.org

53, 61, 101, 173, 233, 257, 277, 433, 569, 677, 757, 829, 857, 881, 937, 953, 997, 1013, 1049, 1093, 1193, 1277, 1297, 1301, 1361, 1381, 1429, 1433, 1693, 1733, 1741, 1873, 1889, 1901, 1993, 2029, 2141, 2161, 2389, 2417, 2549, 2557, 2609

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -208. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[1, 0, 52, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\52), if(isprime(t=w+52*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107162 Primes of the form x^2 + 54y^2.

Original entry on oeis.org

79, 103, 223, 241, 337, 487, 577, 607, 1033, 1153, 1279, 1327, 1399, 1423, 1447, 1471, 1489, 1879, 1993, 2089, 2113, 2311, 2473, 2617, 2647, 2671, 2713, 2719, 2767, 2887, 3079, 3169, 3271, 3313, 3457, 3511, 3559, 3607, 3673, 3697, 3793

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -216. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[1, 0, 54, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\54), if(isprime(t=w+54*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107163 Primes of the form 7x^2 + 8y^2.

Original entry on oeis.org

7, 71, 79, 191, 263, 463, 599, 631, 823, 863, 919, 991, 1031, 1327, 1367, 1471, 1583, 1607, 1831, 1999, 2087, 2111, 2143, 2311, 2543, 2647, 2671, 2767, 2879, 2927, 3119, 3623, 3767, 3823, 4327, 4447, 4463, 4663, 4783, 4799, 4951, 5023, 5119

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -224. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[7, 0, 8, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\7), w=7*x^2; for(y=0, sqrtint((lim-w)\8), if(isprime(t=w+8*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107164 Primes of the form x^2 + 56y^2.

Original entry on oeis.org

137, 233, 281, 449, 673, 953, 977, 1033, 1129, 1409, 1481, 1873, 2017, 2081, 2129, 2137, 2377, 2417, 2657, 2713, 2753, 2857, 2969, 3313, 3529, 3593, 3697, 3833, 4001, 4561, 4649, 4657, 4673, 4729, 4817, 4993, 5657, 5737, 5849, 6217, 6329

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -224. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[1, 0, 56, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\56), if(isprime(t=w+56*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107165 Primes of the form 3x^2 + 19y^2.

Original entry on oeis.org

3, 19, 31, 67, 79, 103, 127, 151, 211, 223, 307, 331, 379, 439, 487, 523, 547, 607, 751, 787, 811, 907, 991, 1039, 1063, 1123, 1171, 1231, 1291, 1399, 1447, 1459, 1471, 1579, 1627, 1663, 1699, 1723, 1747, 1951, 2083, 2131, 2143, 2179, 2203

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -228. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A139827.

[p: p in PrimesUpTo(3000) | p mod 228 in [3, 19, 31, 67, 79, 91, 103, 127, 151, 211, 223]]; // Vincenzo Librandi, Jul 25 2012

QuadPrimes2[3, 0, 19, 10000] (* see A106856 *)

list(lim)=my(v=List([3]), s=[19, 31, 67, 79, 91, 103, 127, 151, 211, 223]); forprime(p=19, lim, if(setsearch(s, p%228), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

The primes are congruent to {3, 19, 31, 67, 79, 91, 103, 127, 151, 211, 223} (mod 228). - T. D. Noe, May 02 2008

A107166 Primes of the form 2x^2 + 29y^2.

Original entry on oeis.org

2, 29, 31, 37, 47, 61, 79, 101, 127, 157, 191, 229, 263, 269, 271, 293, 311, 317, 359, 367, 389, 421, 461, 479, 503, 541, 599, 607, 653, 677, 727, 733, 743, 751, 757, 773, 797, 823, 829, 839, 853, 887, 911, 967, 983, 997, 1013, 1061, 1063, 1087, 1117

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -232. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A139827.

[ p: p in PrimesUpTo(2000) | p mod 232 in {2, 15, 21, 29, 31, 37, 39, 47, 55, 61, 69, 77, 79, 85, 95, 101, 119, 127, 133, 135, 143, 157, 159, 189, 191, 205, 213, 215, 221, 229} ]; // Vincenzo Librandi, Jul 25 2012

QuadPrimes2[2, 0, 29, 10000] (* see A106856 *)

list(lim)=my(v=List([2]), s=[15, 21, 29, 31, 37, 39, 47, 55, 61, 69, 77, 79, 85, 95, 101, 119, 127, 133, 135, 143, 157, 159, 189, 191, 205, 213, 215, 221, 229]); forprime(p=29, lim, if(setsearch(s, p%232), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

The primes are congruent to {2, 15, 21, 29, 31, 37, 39, 47, 55, 61, 69, 77, 79, 85, 95, 101, 119, 127, 133, 135, 143, 157, 159, 189, 191, 205, 213, 215, 221, 229} (mod 232). - T. D. Noe, May 02 2008

A107170 Primes of the form 2x^2 + 31y^2.

Original entry on oeis.org

2, 31, 103, 193, 281, 311, 479, 521, 617, 857, 937, 1063, 1423, 1489, 1657, 1831, 1847, 2543, 2591, 2609, 2671, 2711, 2729, 2753, 2903, 2953, 3023, 3089, 3167, 3319, 3559, 3697, 3761, 3769, 3823, 3863, 4079, 4111, 4201, 4561, 4639, 4903

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -248. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[2, 0, 31, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\31), if(isprime(t=w+31*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

A107171 Primes of the form 5x^2 + 13y^2.

Original entry on oeis.org

5, 13, 97, 137, 193, 197, 457, 593, 613, 617, 733, 877, 1097, 1237, 1373, 1553, 1753, 1877, 1913, 1997, 2273, 2293, 2333, 2377, 2477, 2593, 2917, 2953, 3037, 3373, 3517, 3593, 3673, 3677, 3697, 3733, 3853, 4217, 4337, 4457, 4513, 4517, 4673

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -260. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[5, 0, 13, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\13), if(isprime(t=w+13*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

A107172 Primes of the form 6x^2 + 11y^2.

Original entry on oeis.org

11, 17, 107, 227, 281, 491, 563, 569, 593, 659, 761, 1187, 1289, 1361, 1427, 1451, 1481, 1553, 1811, 1889, 1913, 1931, 2153, 2243, 2273, 2411, 2441, 2459, 2657, 2939, 3203, 3209, 3329, 3449, 3467, 3593, 3761, 3779, 3803, 4259, 4289, 4457

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -264. See A107132 for more information.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[6, 0, 11, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\6), w=6*x^2; for(y=1, sqrtint((lim-w)\11), if(isprime(t=w+11*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

cp's OEIS Frontend

A107158 Primes of the form 3x^2 + 17y^2.

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A107160 Primes of the form x^2 + 52y^2.

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A107162 Primes of the form x^2 + 54y^2.

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A107163 Primes of the form 7x^2 + 8y^2.

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A107164 Primes of the form x^2 + 56y^2.

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A107165 Primes of the form 3x^2 + 19y^2.

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A107166 Primes of the form 2x^2 + 29y^2.

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A107170 Primes of the form 2x^2 + 31y^2.

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A107171 Primes of the form 5x^2 + 13y^2.