A038873 -id:A038873 - cp's OEIS frontend

A141168 Primes of the form 4x^2+9xy-11y^2.

2, 11, 13, 17, 23, 29, 31, 59, 73, 79, 89, 137, 139, 173, 199, 211, 223, 239, 283, 293, 307, 317, 349, 373, 379, 397, 401, 433, 457, 479, 491, 503, 523, 563, 571, 593, 613, 647, 673, 683, 701, 709, 719, 727, 769, 773, 787, 797, 829, 839, 887, 911, 967

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jun 12 2008

nonn

Discriminant = 257. Class = 3. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1

Also primes represented by the improperly equivalent form 11*x^2+9*x*y-4*y^2. - Juan Arias-de-Reyna, Mar 18 2011

			a(5)=23 because we can write 23= 4*2^2+9*2*1-11*1^2

Z. I. Borevich and I. R. Shafarevich, Number Theory

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141167 (d=257).

For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

A141170 Primes of the form x^2+4xy-2y^2 (as well as of the form 3x^2+6xy+y^2).

Original entry on oeis.org

3, 19, 43, 67, 73, 97, 139, 163, 193, 211, 241, 283, 307, 313, 331, 337, 379, 409, 433, 457, 499, 523, 547, 571, 577, 601, 619, 643, 673, 691, 739, 769, 787, 811, 859, 883, 907, 937, 1009, 1033, 1051, 1123, 1129, 1153, 1171, 1201, 1249, 1291, 1297, 1321, 1459, 1483, 1489, 1531

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008

nonn

Discriminant = 24. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also, primes of form u^2 - 6v^2. The transformation {u,v} = {x+2y,y} yields the form in the title. - Tito Piezas III, Dec 31 2008
Conjecture: this is also the list of primes that are simultaneously of the form x^2+2y^2 and of the form x^2+3y^2; that is, the intersection of A002476 and A033203. - Zak Seidov, Jun 07 2014
This is also the list of primes p such that p = 3 or p is congruent to 1 or 19 mod 24. - Jean-François Alcover, Oct 28 2016

			a(2)=19 because we can write 19=3^2+4*3*1-2*1^2 (or 19=3*1^2+6*1*2+2^2)

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141171 (d=24), A106950 (Primes of the form x^2+18y^2), A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Cf. also A242661, A002476, A033203.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

xy[{x_, y_}]:={x^2 + 4 x y - 2 y^2, y^2 + 4 x y - 2 x^2}; Union[Select[Flatten[xy/@Subsets[Range[40], {2}]], #>0&&PrimeQ[#]&]] (* Vincenzo Librandi, Jun 09 2014 *)
Select[Prime[Range[250]], # == 3 || MatchQ[Mod[#, 24], 1|19]&] (* Jean-François Alcover, Oct 28 2016 *)

A141172 Primes of the form 2x^2+2x*y-3y^2 (as well as of the form 2x^2+6xy+y^2).

Original entry on oeis.org

2, 29, 37, 53, 109, 113, 137, 149, 193, 197, 233, 277, 281, 317, 337, 373, 389, 401, 421, 449, 457, 541, 557, 569, 613, 617, 641, 653, 673, 701, 709, 757, 809, 821, 877, 953, 977, 1009, 1033, 1061, 1093, 1117, 1129, 1201, 1213, 1229, 1289, 1297, 1373, 1381, 1409, 1429, 1453, 1481, 1493

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008

nonn

Discriminant = 28. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.
Also, primes of form u^2-7v^2. The transformation {u,v}={3x+y,x} yields the second quadratic form given in the title. - Tito Piezas III, Dec 28 2008
This is also the list of primes p such that p = 2 or p is congruent to 1, 9 or 25 mod 28 - Jean-François Alcover, Oct 28 2016

			a(2)=29 because we can write 29=2*4^2+2*4*3-3*3^2 (or 29=2*1^2+6*1*3+3^2).

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141173 (d=28) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Cf. also A242662.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Select[Prime[Range[250]], # == 2 || MatchQ[Mod[#, 28], 1|9|25]&] (* Jean-François Alcover, Oct 28 2016 *)

A141173 Primes of the form -2x^2+2xy+3y^2 (as well as of the form 6x^2+10xy+3y^2).

Original entry on oeis.org

3, 7, 19, 31, 47, 59, 83, 103, 131, 139, 167, 199, 223, 227, 251, 271, 283, 307, 311, 367, 383, 419, 439, 467, 479, 503, 523, 563, 587, 607, 619, 643, 647, 691, 719, 727, 787, 811, 839, 859, 887, 971, 983, 1039, 1063, 1091, 1123, 1151, 1223, 1231, 1259, 1279, 1291, 1307, 1319, 1399, 1427

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (lourdescm84(AT)hotmail.com), Jun 12 2008

nonn

Discriminant = 28. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also primes of form 7*u^2-v^2. The transformation {u,v}={-x-y,3*x+2*y} yields the form in the title. [Juan Arias-de-Reyna, Mar 19 2011]
This is also the list of primes p such that p = 7 or p is congruent to 3, 19 or 27 mod 28. - Jean-François Alcover, Oct 28 2016

			a(3)=19 because we can write 19=-2*4^2+2*4*3+3*3^2 (or 19=6*1^2+10*1*1+3*1^2).

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141172 (d=28) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Cf. also A242666.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Select[Prime[Range[250]], # == 7 || MatchQ[Mod[#, 28], 3|19|27]&] (* Jean-François Alcover, Oct 28 2016 *)

A141176 Primes of the form 2x^2 + 3xy - 3y^2 (as well as of the form 6x^2 + 9xy + 2y^2).

Original entry on oeis.org

2, 11, 17, 29, 41, 83, 101, 107, 131, 149, 167, 173, 197, 227, 233, 239, 263, 281, 293, 347, 359, 431, 461, 479, 491, 503, 557, 563, 569, 593, 659, 677, 701, 743, 761, 809, 821, 827, 857, 887, 941, 953, 1019, 1031, 1091, 1097, 1151, 1163, 1187, 1217, 1223, 1229, 1283, 1289, 1319, 1361

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008

nonn

Discriminant = 33. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac and gcd(a,b,c) = 1.

These are primes = 11 or congruent to {2, 8, 17, 29, 32} mod 33. Note that the binary quadratic forms with discriminant 33 are in two classes as well as two genera, so there is one class in each genus. A141177 is in the other genus, with primes = 3 or congruent to {1, 4, 16, 25, 31} mod 33. - Jianing Song, Jul 30 2018

			a(3) = 17 because we can write 17 = 2*4^2 + 3*4*5 - 3*5^2 (or 17 = 6*1^2 + 9*1*1 + 2*1^2).

Z. I. Borevich and I. R. Shafarevich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Körper: Eine Einführung in die höhere Zahlentheorie, Springer-Verlag Berlin Heidelberg, 1981, DOI 10.1007/978-3-642-61829-1.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A141177 (d=33); A038872 (d=5); A038873 (d=8); A068228, A141123 (d=12); A038883 (d=13); A038889 (d=17); A141111, A141112 (d=65).

For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Select[Prime[Range[500]], # == 11 || MatchQ[Mod[#, 33], Alternatives[2, 8, 17, 29, 32]]&] (* Jean-François Alcover, Oct 28 2016 *)

A141177 Primes of the form -2x^2 + 3x*y + 3y^2 (as well as of the form 4x^2 + 7xy + y^2).

Original entry on oeis.org

3, 31, 37, 67, 97, 103, 157, 163, 181, 199, 223, 229, 313, 331, 367, 379, 397, 421, 433, 463, 487, 499, 577, 619, 631, 643, 661, 691, 709, 727, 751, 757, 823, 829, 859, 883, 907, 991, 1021, 1039, 1087, 1093, 1123, 1153, 1171, 1213, 1237, 1279, 1291, 1303, 1321, 1423, 1453, 1483

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008

nonn

Discriminant = 33. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac and gcd(a,b,c) = 1.
It is true that A141177(n+1) = A107013(n)? That is: except for p = 3 are these the primes represented by x^2 - x*y + 25*y^2 with x, y nonnegative? - Juan Arias-de-Reyna, Mar 19 2011
From Jianing Song, Jul 30 2018: (Start)
Also primes that are squares modulo 33.
Also primes of the form x^2 - x*y - 8*y^2 with 0 <= x <= y (or x^2 + x*y - 8*y^2 with x, y nonnegative).
These are primes = 3 or congruent to {1, 4, 16, 25, 31} mod 33. Note that the binary quadratic forms with discriminant 33 are in two classes as well as two genera, so there is one class in each genus. A141176 is in the other genus, with primes = 11 or congruent to {2, 8, 17, 29, 32} mod 33.
The observation from Juan Arias-de-Reyna is correct, since the binary quadratic forms with discriminant -99 are also in two classes as well as two genera. Note that -99 = 33*(-3) = (-11)*(-3)^2, so this sequence is essentially the same as A107013.
(End)

			a(2) = 31 because we can write 31 = -2*4^2 + 3*4*3 + 3*3^2 (or 31 = 4*2^2 + 7*2*1 + 1^2).

Z. I. Borevich and I. R. Shafarevich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Körper: Eine Einführung in die höhere Zahlentheorie, Springer-Verlag Berlin Heidelberg, 1981, DOI 10.1007/978-3-642-61829-1.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A141176 (d=33); A038872 (d=5); A038873 (d=8); A068228, A141123 (d=12); A038883 (d=13); A038889 (d=17); A141111, A141112 (d=65).
Cf. A243185 (numbers of the form -2*x^2 + 3*x*y + 3*y^2).
Cf. A107013.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Select[Prime[Range[500]], # == 3 || MatchQ[Mod[#, 33], Alternatives[1, 4, 16, 25, 31]]&] (* Jean-François Alcover, Oct 28 2016 *)

A141179 Primes of the form 3x^2 + 2xy - 3y^2 (as well as of the form 3x^2 + 8xy + 2y^2).

Original entry on oeis.org

2, 3, 5, 13, 37, 43, 53, 67, 83, 107, 157, 163, 173, 197, 227, 277, 283, 293, 307, 317, 347, 373, 397, 443, 467, 523, 547, 557, 563, 587, 613, 643, 653, 677, 683, 733, 757, 773, 787, 797, 827, 853, 877, 883, 907, 947, 997, 1013, 1093, 1117, 1123, 1163, 1187, 1213, 1237, 1277

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina, and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008

nonn

Discriminant = 40. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

For each term p > 5, p^2 == 13^2 (mod 240), and p is of the form 120*k +- b, where b = (13, 37, 43, 53). - Boyd Blundell, Jul 05 2021

			13 is a term because we can write 13 = 3*2^2 + 2*2*1 - 3*1^2 (or 13 = 3*1^2 + 8*1*1 + 2*1^2).

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
Peter Luschny, Binary Quadratic Forms
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141180 (d=40). A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Cf. also A243165.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Select[Prime[Range[250]], # == 2 || # == 5 || MatchQ[Mod[#, 40], Alternatives[3, 13, 27, 37]]&] (* Jean-François Alcover, Oct 28 2016 *)

# uses[binaryQF]
# The function binaryQF is defined in the link 'Binary Quadratic Forms'.
Q = binaryQF([3, 2, -3])
print(Q.represented_positives(1277, 'prime')) # Peter Luschny, Aug 12 2021

A141180 Primes of the form x^2+6xy-y^2 (as well as of the form 6x^2+8x*y+y^2).

Original entry on oeis.org

31, 41, 71, 79, 89, 151, 191, 199, 239, 241, 271, 281, 311, 359, 401, 409, 431, 439, 449, 479, 521, 569, 599, 601, 631, 641, 719, 751, 761, 769, 809, 839, 881, 911, 919, 929, 991, 1009, 1031, 1039, 1049, 1129, 1151, 1201, 1231, 1249, 1279, 1289, 1319, 1321, 1361, 1399, 1409, 1439

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (lourdescm84(AT)hotmail.com), Jun 12 2008

nonn

Discriminant = 40. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac and gcd(a, b, c) = 1.
Also primes of form 10*u^2 - v^2. The transformation {u, v} = {-x, 3*x-y} yields the form in the title, and primes of form U^2 - 10*V^2, with transformation {U, V} = {x+3*y, y}. - Juan Arias-de-Reyna, Mar 19 2011
Therefore, these primes are composite in Q(sqrt(10)), as they can be factored thus: (-u + v*sqrt(10))*(u + v*sqrt(10)). - Alonso del Arte, Jul 22 2012
All primes p such that (p^2 - 1)/24 mod 10 = 0. See A024702.  - Richard R. Forberg, Aug 27 2013

			a(2) = 41 because we can write 41 = 3^2 + 6*3*2 - 2^2 (or 41 = 6*2^2 + 8*2*1 + 1^2). Furthermore, notice that (-7 + 3*sqrt(10))(7 + 3*sqrt(10)) = 41.

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141179 (d=40) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65). A024702.
Cf. also A242664.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Take[Select[Union[Flatten[Table[Abs[a^2 - 10b^2], {a, 0, 49}, {b, 0, 49}]]], PrimeQ], 50] (* Alonso del Arte, Jul 22 2012 *)
Select[Prime[Range[250]], MatchQ[Mod[#, 40], Alternatives[1, 9, 31, 39]]&] (* Jean-François Alcover, Oct 28 2016 *)

Removed defective Mma program. - N. J. A. Sloane, Jun 06 2014

A141182 Primes of the form x^2+6xy-2y^2 (as well as of the form 5x^2+8xy+y^2).

Original entry on oeis.org

5, 37, 53, 89, 97, 113, 137, 157, 181, 229, 257, 269, 313, 317, 353, 389, 397, 401, 421, 433, 449, 509, 521, 577, 617, 641, 653, 661, 709, 757, 773, 797, 829, 881, 929, 977, 1013, 1021, 1049, 1061, 1093, 1109, 1153, 1181, 1193, 1213, 1237, 1277, 1301, 1321, 1373

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (lourdescm84(AT)hotmail.com), Jun 12 2008

nonn

Discriminant = 44. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also, primes of the form u^2 - 11v^2. The transformation {u, v} = {x+3y, y} yields the form in the title. - Tito Piezas III, Dec 28 2008
Also primes p == 1 (mod 4) and == 1, 3, 4, 5 or 9 (mod 11). - Juan Arias-de-Reyna, Mar 20 2011.

			a(3)=53 because we can write 53=5^2+6*5*1-2*1^2 (or 53=5*1^2+8*1*4+4^2)

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141183 (d=44), A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Cf. also A243166.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Select[Prime[Range[250]], MatchQ[Mod[#, 44], Alternatives[1, 5, 9, 25, 37]] &] (* Jean-François Alcover, Oct 28 2016 *)

isA141182(p) = p%4==1 & issquare(Mod(p,11))  \\ M. F. Hasler, Mar 20 2011

A141190 Primes of the form 2x^2+4x*y-5y^2 (as well as of the form 2x^2+8xy+y^2).

Original entry on oeis.org

2, 11, 43, 67, 107, 113, 137, 163, 179, 193, 211, 233, 281, 331, 337, 347, 379, 401, 443, 449, 457, 491, 499, 547, 569, 571, 617, 641, 659, 673, 683, 739, 809, 827, 883, 907, 947, 953, 977, 1009, 1019, 1033, 1051, 1129, 1163, 1171, 1187, 1201, 1283, 1289

Offset: 1

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008

nonn

Discriminant = 56. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

Also primes of the form x^2 + 6xy - 5y^2, cf. A243186. - N. J. A. Sloane, Jun 05 2014

			a(3) = 43 is in the sequence because we can write 43 = 2*4^2 + 4*4*1 - 5*1^2, or 43 = 2*3^2 + 8*3*1 + 1^2.

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A141191 (d=56) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Cf. A243186.
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

xy[{x_, y_}]:={2 x^2 + 4 x y - 5 y^2, 2 y^2 + 4 x y - 5 x^2}; Union[Select[Flatten[xy/@Subsets[Range[50], {2}]], #>0&&PrimeQ[#]&]] (* Vincenzo Librandi, Jun 09 2014 *)

cp's OEIS Frontend

A141168 Primes of the form 4*x^2+9*x*y-11*y^2.

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A141170 Primes of the form x^2+4*x*y-2*y^2 (as well as of the form 3*x^2+6*x*y+y^2).

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A141172 Primes of the form 2*x^2+2*x*y-3*y^2 (as well as of the form 2*x^2+6*x*y+y^2).

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A141173 Primes of the form -2*x^2+2*x*y+3*y^2 (as well as of the form 6*x^2+10*x*y+3*y^2).

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A141176 Primes of the form 2*x^2 + 3*x*y - 3*y^2 (as well as of the form 6*x^2 + 9*x*y + 2*y^2).

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A141177 Primes of the form -2*x^2 + 3*x*y + 3*y^2 (as well as of the form 4*x^2 + 7*x*y + y^2).

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A141179 Primes of the form 3*x^2 + 2*x*y - 3*y^2 (as well as of the form 3*x^2 + 8*x*y + 2*y^2).

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Sage

A141180 Primes of the form x^2+6*x*y-y^2 (as well as of the form 6*x^2+8*x*y+y^2).

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A141168 Primes of the form 4x^2+9xy-11y^2.

A141170 Primes of the form x^2+4xy-2y^2 (as well as of the form 3x^2+6xy+y^2).

A141172 Primes of the form 2x^2+2x*y-3y^2 (as well as of the form 2x^2+6xy+y^2).

A141173 Primes of the form -2x^2+2xy+3y^2 (as well as of the form 6x^2+10xy+3y^2).

A141176 Primes of the form 2x^2 + 3xy - 3y^2 (as well as of the form 6x^2 + 9xy + 2y^2).

A141177 Primes of the form -2x^2 + 3x*y + 3y^2 (as well as of the form 4x^2 + 7xy + y^2).

A141179 Primes of the form 3x^2 + 2xy - 3y^2 (as well as of the form 3x^2 + 8xy + 2y^2).

A141180 Primes of the form x^2+6xy-y^2 (as well as of the form 6x^2+8x*y+y^2).

A141182 Primes of the form x^2+6xy-2y^2 (as well as of the form 5x^2+8xy+y^2).

A141190 Primes of the form 2x^2+4x*y-5y^2 (as well as of the form 2x^2+8xy+y^2).