Expressing a prime as difference between two numbers containing all the previous primes |
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Authors: | Torleiv Kløve |
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Institution: | 1. University of Bergen, Bergen, Norway
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Abstract: | We consider the simultaneous equations $$\begin{gathered} p_1^{\alpha _1 } p_2^{\alpha _2 } ...p_n^{\alpha _n } = P_1 P_2 \hfill \\ p_{n + 1} = P_1 - P_2 \hfill \\ \end{gathered} $$ wherep 1,p 2,...,p n+1 are then+1 first primes and α1,...,α n ,P 1,P 2 are integers. The equations are solved completely forn≦3 and all solutions given under certain restrictions on the α i 's forn≦9. |
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