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等差素数列について Notes on Arithmetic Progressions of Prime Numbers 洞田, 勝博 ホラタ, カツヒロ 洞田 ホラタ 勝博 カツヒロ 篠原, 雅史 シノハラ, マサシ 酒井, 幸吉 サカイ, コウキチ P(論文) A finite ncreasing sequence {pn}, (n=1, 2, 3, ・・・, t) of prime numbers, (t〓3), is called an arithmetic progression of primes with a common differnce d, denoted by Ap(p_1) or Ap(p_1, d), if p_<k+1>-p_k=d∀k, 1〓k〓t-1 and p_t+d is a composite number. Then t is called the size of Ap(p_1). Ap(2) does not exist. For any Ap(p_1, d), prime p>2, its size is at most p, and d is an even number different from multiples of p. In this note we report various data on arithmetic progressions of primes gathered from long computation using personal computers. For example the following Ap(p, d) given the pairs (p, d) are of size 14, which are the largest size among primes p<10^7 and common differnces d<10^8. [table] We propose the following Conjecture For any prime p>2 we have 1) There exist infinitely many Ap(P). 2) There exist an Ap(P) of size p. The above 2) is true for p=3, 5, 7, 11. 2007-03-31 jpn departmental bulletin paper https://kjunshin.repo.nii.ac.jp/records/199 AA12012192 国際人間学部紀要 International human studies 13 81 99 https://kjunshin.repo.nii.ac.jp/record/199/files/HORATA-KO13.pdf application/pdf 818.8 kB 2007-03-31