Adleman, L. M. and Huang, M. A. "Recognizing Primes in Random Polynomial Time." In Proc. 19th STOC, New York City, May 25-27, 1986. New York: ACM Press, pp. 462-469, 1987.Alpern, D. "Factorization Using the Elliptic Curve Method." http://www.alpertron.com.ar/ECM.HTM.Atkin, A. O. L. Lecture notes of a conference, Boulder, CO, Aug. 1986.Atkin, A. O. L. and Morain, F. "Elliptic Curves and Primality Proving." Res. Rep. 1256, INRIA, June 1990.Atkin, A. O. L. and Morain, F. "Elliptic Curves and Primality Proving." Math. Comput.61, 29-68, 1993.Bosma, W. "Primality Testing Using Elliptic Curves." Techn. Rep. 85-12, Math. Inst., Univ. Amsterdam, 1985.Chudnovsky, D. V. and Chudnovsky, G. V. "Sequences of Numbers Generated by Addition in Formal Groups and New Primality and Factorization Tests." Res. Rep. RC 11262, IBM, Yorktown Heights, NY, 1985.Cohen, H. Cryptographie, factorisation et primalité: l'utilisation des courbes elliptiques. Paris: C. R. J. Soc. Math. France, Jan. 1987.Kaltofen, E.; Valente, R.; and Yui, N. "An Improved Las Vegas Primality Test." Res. Rep. 89-12, Rensselaer Polytechnic Inst., Troy, NY, May 1989.Martin, M. "PRIMO--Primality Proving." http://www.ellipsa.net.Martin, M. "20 Greatest Candidates Verified with Primo." http://www.ellipsa.net/primo/top20.html.Underwood, P. "R49081 is Prime!" Mar. 21, 2022. https://mersenneforum.org/showpost.php?p=602219&postcount=35.
。截至 2004 年，程式PRIMO可以使用這種技術在 1 GHz 處理器上大約 2000 小時的計算（或近三個月的不間斷計算）中驗證一個 4769 位數的素數。截至 2009 年，使用此技術驗證的最大的素數是第 11 個 Mills 素數 (http://primes.utm.edu/primes/page.php?id=77907)
位十進位制數字。該證明是透過分散式計算執行的，該計算始於 2005 年 9 月，結束於 2006 年 6 月，需要累積 CPU 時間，相當於 2.39 GHz 執行 2219 天（略多於 6 年）。
(https://primes.utm.edu/primes/page.php?id=133761) 是素數。認證在配備 64 核的 AMD 3990x 計算機上花費了 20 個月，驗證花費了大約 13 個小時 (Underwood 2022)。