Chen, J. R. "On the Distribution of Almost Primes in an Interval." Sci. Sinica18, 611-627, 1975.Euler, L. "De numeris primis valde magnis." Novi Commentarii academiae scientiarum Petropolitanae9, 99-153, (1760) 1764. Reprinted in Commentat. arithm.1, 356-378, 1849. Reprinted in Opera Omnia: Series 1, Volume 3, pp. 1-45.Goldman, J. R. The Queen of Mathematics: An Historically Motivated Guide to Number Theory. Wellesley, MA: A K Peters, p. 22, 1998.Hardy, G. H. and Wright, W. M. "Unsolved Problems Concerning Primes." §2.8 and Appendix §3 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, pp. 19 and 415-416, 1979.Iwaniec, H. and Pintz, J. "Primes in Short Intervals." Monatsh. f. Math.98, 115-143, 1984.Ogilvy, C. S. Tomorrow's Math: Unsolved Problems for the Amateur, 2nd ed. Oxford, England: Oxford University Press, p. 116, 1972.Ribenboim, P. The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 132-134 and 206-208, 1996.Sloane, N. J. A. Sequences A002496/M1506, A005574/M1010, and A007491/M1389 in "The On-Line Encyclopedia of Integer Sequences."
，都存在一个素数 
介于 
和 
之间 (Hardy and Wright 1979, p. 415; Ribenboim 1996, pp. 397-398)，以及
形如 
(Euler 1760; Mirsky 1949; Hardy and Wright 1979, p. 19; Ribenboim 1996, pp. 206-208)。前几个这样的素数是 2, 5, 17, 37, 101, 197, 257, 401, ... (OEIS A002496)。
之间是否总是存在素数 
和 
，但陈 (Chen) (1975) 已经证明，一个数 
（它是素数或半素数）总是满足这个不等式。此外，在 
和 
之间总是存在素数，其中 
(Iwaniec 和 Pintz 1984; Hardy 和 Wright 1979, p. 415)。对于 
, 2, ..., 介于 
和 
之间的最小素数是 2, 5, 11, 17, 29, 37, 53, 67, 83, ... (OEIS A007491)。
（形如 
）由 2, 5, 17, 37, 101, 197, 257, 401, ... 给出 (OEIS A002496)。这些对应于 
, 2, 4, 6, 10, 14, 16, 20, ... (OEIS A005574; Hardy 和 Wright 1979, p. 19)。