Editing Regular prime (section)

=== Infinitude ===
[[Kaj Løchte Jensen|K. L. Jensen]] (a student of [[Niels Nielsen (mathematician)|Niels Nielsen]]<ref>[http://tau.ac.il/~corry/publications/articles/pdf/Computers%20and%20FLT.pdf Leo Corry: Number Crunching vs. Number Theory: Computers and FLT, from Kummer to SWAC (1850–1960), and beyond]</ref>) proved in 1915 that there are infinitely many irregular primes of the form {{nowrap|4''n'' + 3}}.<ref>{{cite journal | last = Jensen | first = K. L. | title = Om talteoretiske Egenskaber ved de Bernoulliske Tal | jstor=24532219 | journal = NYT Tidsskr. Mat. | volume = B 26 | pages = 73–83 | year = 1915}}</ref>
In 1954 [[Leonard Carlitz|Carlitz]] gave a simple proof of the weaker result that there are in general infinitely many irregular primes.<ref>{{cite journal | last = Carlitz | first = L. | title = Note on irregular primes | journal = Proceedings of the American Mathematical Society | volume = 5 | issue = 2 | pages = 329–331 | publisher = [[American Mathematical Society|AMS]] | year = 1954 | url = https://www.ams.org/journals/proc/1954-005-02/S0002-9939-1954-0061124-6/S0002-9939-1954-0061124-6.pdf  | issn = 1088-6826 | doi = 10.1090/S0002-9939-1954-0061124-6 | mr = 61124| doi-access = free}}</ref>

Metsänkylä proved in 1971 that for any integer {{nowrap|''T'' > 6}}, there are infinitely many irregular primes not of the form {{nowrap|''mT'' + 1}} or {{nowrap|''mT'' − 1}},<ref>{{cite journal |author=Tauno Metsänkylä |title=Note on the distribution of irregular primes |journal=Ann. Acad. Sci. Fenn. Ser. A I |volume=492 |year=1971 |mr=0274403}}</ref> and later generalized this.<ref>{{cite journal |author=Tauno Metsänkylä |title=Distribution of irregular prime numbers |journal=Journal für die reine und angewandte Mathematik |volume=1976 |issue=282 |doi=10.1515/crll.1976.282.126 |url=http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002191873 |year=1976|pages=126–130 |s2cid=201061944 }}</ref>