A140633 -id:A140633 - cp's OEIS frontend

A139990 Primes of the form 12x^2+12xy+73y^2.

73, 97, 313, 433, 577, 937, 1153, 1657, 1753, 1777, 1993, 2113, 2593, 2617, 2833, 2953, 3433, 3457, 3673, 3793, 4177, 4273, 4297, 4513, 5113, 5857, 5953, 6793, 7297, 7537, 7873, 7993, 8377, 8713, 9337, 9817, 10177, 10513, 10657, 10993

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-3360. See A139827 for more information.

Also primes of the forms 48*x^2+24*x*y+73*y^2 and 33*x^2+12*x*y+52*y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(11000) | p mod 840 in [73, 97, 313, 433, 577, 817]]; // Vincenzo Librandi, Aug 03 2012

QuadPrimes2[12, -12, 73, 10000] (* see A106856 *)

The primes are congruent to {73, 97, 313, 433, 577, 817} (mod 840).

A139991 Primes of the form 15x^2+56y^2.

Original entry on oeis.org

71, 191, 239, 359, 431, 599, 911, 1031, 1439, 1871, 2039, 2111, 2591, 2711, 2879, 3119, 3719, 4271, 4391, 4799, 5231, 5279, 5399, 5471, 5639, 6311, 6791, 6911, 6959, 7079, 7151, 7919, 8831, 8999, 9311, 9431, 9479, 9839, 10151, 10271, 11159

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-3360. See A139827 for more information.

Also primes of the forms 39x^2+12xy+44y^2 and 36x^2+12xy+71y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 840 in [71, 191, 239, 359, 431, 599]]; // Vincenzo Librandi, Aug 03 2012

QuadPrimes2[15, 0, 56, 10000] (* see A106856 *)

The primes are congruent to {71, 191, 239, 359, 431, 599} (mod 840).

A139992 Primes of the form 20x^2+20xy+47y^2.

Original entry on oeis.org

47, 167, 383, 503, 647, 887, 983, 1223, 1487, 1823, 1847, 2063, 2663, 2687, 2903, 3023, 3167, 3407, 3527, 3863, 4007, 4583, 4703, 5087, 5927, 6047, 6263, 6863, 7103, 7607, 7703, 7727, 8447, 8543, 8783, 9623, 9743, 9887, 10223, 10247, 10463

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-3360. See A139827 for more information.

Also primes of the forms 47x^2+40xy+80y^2 and 47x^2+42xy+63y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 840 in [47, 143, 167, 383, 503, 647]]; // Vincenzo Librandi, Aug 03 2012

QuadPrimes2[20, -20, 47, 10000] (* see A106856 *)

The primes are congruent to {47, 143, 167, 383, 503, 647} (mod 840).

A139993 Primes of the form 21x^2+40y^2.

Original entry on oeis.org

61, 181, 229, 349, 661, 829, 1021, 1069, 1669, 1741, 1861, 2029, 2341, 2749, 3181, 3541, 3709, 4021, 4261, 4549, 4861, 5101, 5701, 5869, 6229, 6709, 6781, 6949, 7069, 7549, 7621, 7741, 7789, 8221, 8389, 8461, 8581, 8629, 9421, 9901, 10069

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-3360. See A139827 for more information.

Also primes of the form 45x^2+30xy+61y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 840 in [61, 181, 229, 349, 661, 829]]; // Vincenzo Librandi, Aug 03 2012

QuadPrimes2[21, 0, 40, 10000] (* see A106856 *)

The primes are congruent to {61, 181, 229, 349, 661, 829} (mod 840).

A139996 Primes of the form 28x^2+28xy+37y^2.

Original entry on oeis.org

37, 277, 373, 613, 757, 877, 1093, 1117, 1213, 1453, 1597, 1933, 2053, 2293, 2437, 2557, 2797, 3613, 3637, 3733, 4813, 4957, 5077, 5413, 5653, 6133, 6637, 6997, 7333, 7477, 7933, 8317, 8677, 9013, 9157, 9277, 9613, 10333, 10357, 10453, 10837

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-3360. See A139827 for more information.

Also primes of the forms 37x^2+18xy+93y^2 and 37x^2+24xy+72y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 840 in [37, 253, 277, 373, 613, 757]]; // Vincenzo Librandi, Aug 03 2012

QuadPrimes2[28, -28, 37, 10000] (* see A106856 *)

The primes are congruent to {37, 253, 277, 373, 613, 757} (mod 840).

A140003 Primes of the form 8x^2+8xy+167y^2.

Original entry on oeis.org

167, 263, 503, 743, 887, 1223, 1487, 1583, 1823, 1847, 2063, 2087, 2207, 2543, 2903, 3167, 3407, 3527, 3863, 4127, 4463, 4583, 4703, 4967, 5783, 5807, 5903, 6047, 6287, 6863, 7103, 7127, 7487, 7607, 7823, 8087, 8423, 8447, 8543, 8663

Offset: 1

T. D. Noe, May 02 2008

Discriminant = -5280. See A139827 for more information.

Also primes of the forms 32x^2+16xy+167y^2 and 32x^2+24xy+87y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 1320 in [167, 263, 503, 527, 623, 743, 767, 887, 1007, 1223]]; // Vincenzo Librandi, Aug 04 2012

QuadPrimes2[8, -8, 167, 10000] (* see A106856 *)

The primes are congruent to {167, 263, 503, 527, 623, 743, 767, 887, 1007, 1223} (mod 1320).

A140008 Primes of the form 24x^2+55y^2.

Original entry on oeis.org

79, 151, 271, 439, 919, 1231, 1399, 1471, 1759, 1999, 2239, 2551, 2719, 2791, 3079, 3319, 3511, 3559, 4111, 4231, 4639, 4759, 4831, 5431, 6079, 6151, 6199, 6679, 6871, 6991, 7039, 8191, 8311, 8599, 8719, 8839, 9151, 9319, 9391, 9511, 9631

Offset: 1

T. D. Noe, May 02 2008

Discriminant = -5280. See A139827 for more information.

Also primes of the form 39x^2+36xy+76y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 1320 in [79, 151, 271, 391, 439, 679, 799, 871, 919, 1231]]; // Vincenzo Librandi, Aug 04 2012

QuadPrimes2[24, 0, 55, 10000] (* see A106856 *)

The primes are congruent to {79, 151, 271, 391, 439, 679, 799, 871, 919, 1231} (mod 1320).

A140010 Primes of the form 33x^2+40y^2.

Original entry on oeis.org

73, 193, 337, 457, 673, 937, 1033, 1297, 1657, 1777, 1993, 2593, 2617, 2713, 2833, 2857, 3313, 3673, 4153, 4177, 4297, 4993, 5233, 5737, 5953, 6217, 6553, 6577, 6673, 6793, 7057, 7537, 7873, 7993, 8377, 9433, 9697, 10177, 10273, 10513, 10753

Offset: 1

T. D. Noe, May 02 2008

Discriminant = -5280. See A139827 for more information.

Also primes of the form 52x^2+36xy+57y^2. See A140633. - T. D. Noe, May 19 2008

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)

[p: p in PrimesUpTo(12000) | p mod 1320 in [73, 193, 217, 337, 457, 673, 937, 1033, 1273, 1297]]; // Vincenzo Librandi, Aug 04 2012

QuadPrimes2[33, 0, 40, 10000] (* see A106856 *)

The primes are congruent to {73, 193, 217, 337, 457, 673, 937, 1033, 1273, 1297} (mod 1320).

A140613 Primes of the form 7x^2 + 6xy + 39y^2.

Original entry on oeis.org

7, 79, 127, 151, 271, 439, 607, 919, 967, 1063, 1231, 1327, 1399, 1447, 1471, 1663, 1759, 1999, 2239, 2287, 2383, 2503, 2551, 2647, 2719, 2767, 2791, 3079, 3319, 3343, 3511, 3559, 3583, 3607, 3823, 3847, 3967, 4111, 4231, 4567, 4639, 4663

Offset: 1

T. D. Noe, May 19 2008

Discriminant=-1056. Also primes of the form 7x^2 + 4xy + 76y^2.

In base 12, the sequence is 7, 67, X7, 107, 1X7, 307, 427, 647, 687, 747, 867, 927, 987, X07, X27, E67, 1027, 11X7, 1367, 13X7, 1467, 1547, 1587, 1647, 16X7, 1727, 1747, 1947, 1E07, 1E27, 2047, 2087, 20X7, 2107, 2267, 2287, 2367, 2467, 2547, 2787, 2827, 2847, where X is 10 and E is 11. Moreover, the discriminant is -740. - Walter Kehowski, Jun 01 2008

Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi, next 5218 terms from N. J. A. Sloane]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
J. Voight, Quadratic forms that represent almost the same primes, Math. Comp., Vol. 76 (2007), pp. 1589-1617. See Example 6.1. - _N. J. A. Sloane_, Jun 07 2014

Cf. A140633.

Union[QuadPrimes2[7, 6, 39, 10000], QuadPrimes2[7, -6, 39, 10000]] (* see A106856 *)

select(n-> n%264==7 || n%264==79 || n%264==127 || n%264==151 || n%264==175, primes(100000)) \\ N. J. A. Sloane, Jun 07 2014

These are exactly the primes congruent to one of 7, 79, 127, 151, or 175 (mod 264) [Voight]. - N. J. A. Sloane, Jun 07 2014

Incorrect Mathematica program deleted by N. J. A. Sloane, Jun 07 2014

A140614 Primes of the form 15x^2+12xy+20y^2.

Original entry on oeis.org

23, 47, 71, 191, 311, 383, 599, 647, 719, 839, 863, 911, 983, 1103, 1367, 1439, 1511, 1607, 1871, 2039, 2399, 2423, 2447, 2663, 2687, 2711, 2927, 3023, 3191, 3359, 3623, 3719, 3767, 4007, 4079, 4271, 4679, 4799, 4871, 4943, 5039, 5087, 5303

Offset: 1

T. D. Noe, May 19 2008

Discriminant=-1056. Also primes of the form 23x^2+12xy+36y^2.

In base 12 the sequence is 1E, 3E, 5E, 13E, 21E, 27E, 41E, 45E, 4EE, 59E, 5EE, 63E, 69E, 77E, 95E, 9EE, X5E, E1E, 10EE, 121E, 147E, 149E, 14EE, 165E, 167E, 169E, 183E, 18EE, 1X1E, 1E3E, 211E, 219E, 221E, 239E, 243E, 257E, 285E, 293E, 299E, 2X3E, 2XEE, 2E3E, 309E, where X is 10 and E is 11. Moreover, the discriminant is -740. - Walter Kehowski, May 31 2008

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. A140633.

Union[QuadPrimes2[15, 12, 20, 10000], QuadPrimes2[15, -12, 20, 10000]] (* see A106856 *)

cp's OEIS Frontend

A139990 Primes of the form 12*x^2+12*x*y+73*y^2.

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A139991 Primes of the form 15x^2+56y^2.

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A139992 Primes of the form 20x^2+20xy+47y^2.

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A139993 Primes of the form 21x^2+40y^2.

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A139996 Primes of the form 28x^2+28xy+37y^2.

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A140003 Primes of the form 8x^2+8xy+167y^2.

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Magma

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A140008 Primes of the form 24x^2+55y^2.

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Magma

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A140010 Primes of the form 33x^2+40y^2.

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Magma

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A139990 Primes of the form 12x^2+12xy+73y^2.

A140613 Primes of the form 7x^2 + 6xy + 39y^2.