In this paper, we give out the formula of number of primes no more than any given n (n ∈ Z<sup>+</sup>, n > 2). At the same time, we also show the principle, derivation process of the formula and appli...In this paper, we give out the formula of number of primes no more than any given n (n ∈ Z<sup>+</sup>, n > 2). At the same time, we also show the principle, derivation process of the formula and application examples, it is usually marked with π(n), which is: that is: where “[ ]” denotes taking integer. r = 1,2,3,4,5,6;s<sub>x</sub> = s<sub>1</sub>,s<sub>2</sub>,...,s<sub>j</sub>,s<sub>h</sub>;s1</sub>,s2</sub>,...,s<sub>j</sub>,,s<sub>h </sub><sub>= 0,1,2,3,....</sub>As i ≥ 2, 2 ≤ s<sub>x </sub>≤ i-1 (x=1,2,...,j,h).展开更多
There are settings where encryption must be performed by a sender under a time constraint. This paper de-scribes an encryption/decryption algorithm based on modular arithmetic of complex integers called Gaus-sians. It...There are settings where encryption must be performed by a sender under a time constraint. This paper de-scribes an encryption/decryption algorithm based on modular arithmetic of complex integers called Gaus-sians. It is shown how cubic extractors operate and how to find all cubic roots of the Gaussian. All validations (proofs) are provided in the Appendix. Detailed numeric illustrations explain how to use the method of digital isotopes to avoid ambiguity in recovery of the original plaintext by the receiver.展开更多
文摘In this paper, we give out the formula of number of primes no more than any given n (n ∈ Z<sup>+</sup>, n > 2). At the same time, we also show the principle, derivation process of the formula and application examples, it is usually marked with π(n), which is: that is: where “[ ]” denotes taking integer. r = 1,2,3,4,5,6;s<sub>x</sub> = s<sub>1</sub>,s<sub>2</sub>,...,s<sub>j</sub>,s<sub>h</sub>;s1</sub>,s2</sub>,...,s<sub>j</sub>,,s<sub>h </sub><sub>= 0,1,2,3,....</sub>As i ≥ 2, 2 ≤ s<sub>x </sub>≤ i-1 (x=1,2,...,j,h).
文摘There are settings where encryption must be performed by a sender under a time constraint. This paper de-scribes an encryption/decryption algorithm based on modular arithmetic of complex integers called Gaus-sians. It is shown how cubic extractors operate and how to find all cubic roots of the Gaussian. All validations (proofs) are provided in the Appendix. Detailed numeric illustrations explain how to use the method of digital isotopes to avoid ambiguity in recovery of the original plaintext by the receiver.
