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{\bf In the fourth extended version of this article, we provide acomprehensive historical survey of 200 different proofs of famous Euclid'stheorem on the infinitude of prime numbers (300 {\small B.C.}--2022)}. Theauthor is trying to collect almost all the known proofs on infinitude ofprimes, including some proofs that can be easily obtained as consequences ofsome known problems or divisibility properties. Furthermore, here are listednumerous elementary proofs of the infinitude of primes in different arithmeticprogressions.  All the references concerning the proofs of Euclid's theorem that use similarmethods and ideas are exposed subsequently. Namely, presented proofs aredivided into the first five subsections of Section 2 in dependence of themethods that are used in them. 14 proofs which are proved from 2012 to 2017 aregiven in Subsection 2.9, and 18 recent proofs from 2018 to 2022 are presentedin Subsection 2.10.  In Section 3, we mainly survey elementary proofs of the infinitude of primesin different arithmetic progressions. Presented proofs are special cases ofDirichlet's theorem. In Section 4, we give a new simple ''Euclidean's proof''of the infinitude of primes.

Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.--2022) and another new proof