## What is/are Small Prime?

Small Prime - In the third paper in a series of papers on autism savants, detection of giftedness and the use of mental arithmetic as an intervention in autism and a practice of metal wellness, we describe the use of python scripts towards primality detection exercises, of both small primes and arbitrary sized numbers and several other exercises including sequence prediction, inspired by branch prediction architectures.^{[1]}We establish estimates for the number of ways to represent any reduced residue class as a product of a prime and an integer free of small prime factors.

^{[2]}In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.

^{[3]}Real-world examples of periodical species range from cicadas, whose life cycles are large prime numbers, like 13 or 17, to bamboos, whose periods are large multiples of small primes, like 40 or even 120.

^{[4]}Typically, the algorithms used have two parts – trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites.

^{[5]}We consider the {\it noisy polynomial interpolation problem\/} of recovering an unknown $s$-sparse polynomial $f(X)$ over the ring $\mathbb Z_{p^k}$ of residues modulo $p^k$, where $p$ is a small prime and $k$ is a large integer parameter, from approximate values of the residues of $f(t) \in \mathbb Z_{p^k}$.

^{[6]}We say a non-zero submodule E of D is d-small prime if for each c ∈ R, d ∈ D, (d) «d D with cd ∈ E, then either d ∈ E or c ∈ [E: D] and an fi-module D is a d-small prime if annD = annE for each non-zero submodule E d-small in D.

^{[7]}Fourier transforms whose sizes are powers of two or have only small prime factors have been extensively studied, and optimized implementations are typically memory-bound.

^{[8]}We give an algorithm that computes those degrees in the manner of the Pohlig and Hellman algorithm ( 1978 ) for computing discrete logarithms modulo a prime number p when the factorization of p − 1 (or p + 1 ) has small prime factors, that is, when p − 1 (or p + 1 ) is smooth.

^{[9]}Small prime-sized discrete Fourier transforms appear in various applications from quantum mechanics, material sciences and machine learning.

^{[10]}The proof uses the algorithm of Guardia, Montes and Nart to calculate an integral basis and then finds integral elements of small prime power norm to establish an upper bound for the class number; further algebraic arguments prove the class number is 1.

^{[11]}The only work on construction of self-dual NMDS codes shows existence of

^{[12]}We prove the following uniform congruence counting theorem with respect to the family of Euclidean norm balls BR in M2(R) of radius R: for all positive integer q with no small prime factors, #(Γ(q)∩BR)=cΓR2δ#(SL2(Z/qZ))+O(qCR2δ−ϵ) as R→∞ for some cΓ>0,C>0,ϵ>0 which are independent of q.

^{[13]}Let p be a small prime and n = n 1 n 2 > 1 be a composite integer.

^{[14]}Hence, our attack does not require the incremental prime search assumption and is applicable when countermeasures against previous attacks are deployed since it also does not require the assumption of trial divisions with small primes on prime candidates.

^{[15]}Such constructions are usually based on CLT13 multilinear maps, since CLT13 inherently provides a composite encoding space, with a plaintext ring \(\bigoplus _{i=1}^n \mathbb {Z}/g_i\mathbb {Z}\) for small primes \(g_i\)’s.

^{[16]}We first prove that the decision and search versions are equivalent provided q is a small prime.

^{[17]}Given a non-isotrivial elliptic curve over ℚ(t) with large Mordell–Weil rank, we explain how one can build, for suitable small primes p, infinitely many fields of degree p2 − 1 whose ideal class gr.

^{[18]}In the first part, we report the usage of the small prime difference method of the form | b 2 p − a 2 q | < N γ where the ratio of q p is close to b 2 a 2 , which yields a bound d < 3 2 N 3 4 − γ from the convergents of the continued fraction expansion of e N − ⌈ a 2 + b 2 a b N ⌉ + 1.

^{[19]}

## small prime factor

We establish estimates for the number of ways to represent any reduced residue class as a product of a prime and an integer free of small prime factors.^{[1]}Typically, the algorithms used have two parts – trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites.

^{[2]}Fourier transforms whose sizes are powers of two or have only small prime factors have been extensively studied, and optimized implementations are typically memory-bound.

^{[3]}We give an algorithm that computes those degrees in the manner of the Pohlig and Hellman algorithm ( 1978 ) for computing discrete logarithms modulo a prime number p when the factorization of p − 1 (or p + 1 ) has small prime factors, that is, when p − 1 (or p + 1 ) is smooth.

^{[4]}We prove the following uniform congruence counting theorem with respect to the family of Euclidean norm balls BR in M2(R) of radius R: for all positive integer q with no small prime factors, #(Γ(q)∩BR)=cΓR2δ#(SL2(Z/qZ))+O(qCR2δ−ϵ) as R→∞ for some cΓ>0,C>0,ϵ>0 which are independent of q.

^{[5]}