Geodesic
Primes are nonnegative values of a polynomial in 10 variables
Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part II, Tome 68 (1977), pp. 62-82

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A polynomial with integer coefficients of 10 variables is constructed, whose set of all nonnegative values (for positive integer values of the variables) is precisely the set of all prime numbers. 
@article{ZNSL_1977_68_a6,
     author = {Yu. V. Matiyasevich},
     title = {Primes are nonnegative values of a polynomial in 10 variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {62--82},
     publisher = {mathdoc},
     volume = {68},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_68_a6/}
}
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Yu. V. Matiyasevich. Primes are nonnegative values of a polynomial in 10 variables. Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part II, Tome 68 (1977), pp. 62-82. http://geodesic.mathdoc.fr/item/ZNSL_1977_68_a6/