Infinite Cunningham Chains and Infinite Arithmetic Primes
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- Chandra matrix, Cunningham Chain, Arithmetic Primes, Flgamal Signature, Pesticide Residual
- Mi Zhou; Jun Steed Huang; Yiwen Xia
- This paper shows a fairly simple method of using Chandra matrices to explain the property of Cunningham chains that are related to Green-Tao theorem, which states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The main reason we study this relationship is to find a systematic computation method for finding the large safe prime which is needed for construction of the Elgamal signature scheme for an agriculture application. In this paper, it shows that the density of safe primes are uniform in logarithm scale, we plot them with Matlab program. From which, we can see that the collection of the primes obtained from the Chandra matrices approach can be used for the set of signatures for the pesticide residue testing certificate, across a number of products demanding progressively different level of residual concentrations.
Full text: IJISM_522_FINAL.pdf