摘  要:本文從素數的基本概念出發，介紹了素數有無窮多個的性質，并且給出了一些偉大的數學家給出的關于素數有無窮多個的幾個新證明，如歐幾里德、歌德巴赫、歐拉等數學家對素數無窮多的的獨特的證明，至今被后人稱道。千百年人們對素數作了艱難的探索并得出了一些杰出的成果，但關于素數的一些猜想至今仍未得到證明，可見這個領域還是較為有討論價值的.本文將展示前人的一些偉大成果，旨在使讀者對素數、素數無窮多有一個較全面的了解，并爭取在研究過程中有新的突破。

關鍵詞：素數； 無窮多； 反證法；N2+1形素數； 4n+1形素數。

Abstract:This paper from the basic concept of prime, introduces the properties of an infinite number of primes, and gives some great mathematicians give about an infinite number of primes, several new proofs, such as Euclid, GeDeBaHe, euler infinite number of primes such mathematician the unique proof, so far to be remembered praised. Thousands of people to make the tough exploration prime and obtained some outstanding achievements, but some guesses about primes have so far not been proofed, visible in this area or more. This paper will show some of the great achievements, predecessors to primes, aims to make readers have a prime infinite, and more comprehensive understanding in the process of research for a new breakthrough.

Key words：prime; infinite; proof by contradiction; N2+1Figured primes;  4n+1Figured primes.