Geodesic
Infinite sets of primes, admitting Diophantine representations in eight variables
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IX, Tome 220 (1995), pp. 36-48

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The existence of infinite sets of primes which can be repesented as the sets of positive values of some polynomials in a small number of variables is discussed. (All variables range over positive integers.) It is proved (noneffectively) that there exists such a set, which has a representation with eight variables. This number of variables is smaller than in the best universal construction known today, which is ten. Also, some improvements of well-known technical lemmas are given. Bibliography: 16 titles. 
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     author = {M. A. Vsemirnov},
     title = {Infinite sets of primes, admitting {Diophantine} representations in eight variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--48},
     publisher = {mathdoc},
     volume = {220},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_220_a2/}
}
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M. A. Vsemirnov. Infinite sets of primes, admitting Diophantine representations in eight variables. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IX, Tome 220 (1995), pp. 36-48. http://geodesic.mathdoc.fr/item/ZNSL_1995_220_a2/