Geodesic
On the congruence for twice the primes
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 33, Tome 470 (2018), pp. 138-146 
B. B. Lurj'e; A. M. Poretsky. On the congruence for twice the primes. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 33, Tome 470 (2018), pp. 138-146. http://geodesic.mathdoc.fr/item/ZNSL_2018_470_a8/
@article{ZNSL_2018_470_a8,
     author = {B. B. Lurj'e and A. M. Poretsky},
     title = {On the congruence for twice the primes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--146},
     year = {2018},
     volume = {470},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_470_a8/}
}
TY  - JOUR
AU  - B. B. Lurj'e
AU  - A. M. Poretsky
TI  - On the congruence for twice the primes
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 138
EP  - 146
VL  - 470
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_470_a8/
LA  - ru
ID  - ZNSL_2018_470_a8
ER  - 
%0 Journal Article
%A B. B. Lurj'e
%A A. M. Poretsky
%T On the congruence for twice the primes
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 138-146
%V 470
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_470_a8/
%G ru
%F ZNSL_2018_470_a8

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The article proposes an elementary necessary condition for doubles prime integers to be congruent.

[1] B. B. Lure, “O kongruentnosti prostykh chisel”, Zap. nauchn. semin. POMI, 455, 2017, 84–90

[2] N. Koblits, Vvedenie v ellipticheskie krivye i modulyarnye formy, Mir, 1988

[3] B. J. Birch, “Diophantine analysis and modular functions”, Conf. Algebraic Geometry, Tata Institute, Bombay, 1968

[4] K. Heegner, “Diophantische Analysis und Modulfunktionen”, Math. Zeitschrift, 56:3 (1952), 227–253 | DOI | MR | Zbl

[5] P. Monsky, “Mock Heegner points and congruent numbers”, Math. Zeitschrift, 204:1 (1990), 45–67 | DOI | MR | Zbl

[6] Ye Tian, Congruent numbers and Heegner points, 2012, arXiv: 1210.8231 | MR

[7] Ye Tian, Yuan Xinyi, Zhang Shouwu, Genus periods, genus points and congruent number problem, 2014, arXiv: 1411.4728 | MR

[8] Tunnell, B. Jerrold, “A classical Diophantine problem and modular forms of weight $3/2$”, Invent. Math., 72:2 (1983), 323–334 | DOI | MR | Zbl