# Prime Simplicity

## Related Articles

- A REMARK ON PARTIAL SUMS INVOLVING THE MÃ–BIUS FUNCTION. Tao, Terence // Bulletin of the Australian Mathematical Society;Apr2010, Vol. 81 Issue 2, p343
Let (P)âŠ‚N be a multiplicative subsemigroup of the natural numbers N = {1,2,3,â€¦} generated by an P arbitrary set P of primes (finite or infinite). We give an elementary proof that the partial sums Î£n�xCE;(P):nâ©½x(Î¼(n))/n are bounded in magnitude by 1. With the aid of the...

- HOW MANY FACTORS? Dias, Lücia Braz // Mathematics in School;Mar2005, Vol. 34 Issue 2, p30
Provides information on predicting the number of factors of a number. Overview of a table on powers of primes and its products regarding the factorization; Construction of a model for a whole number and its factors; Significance of the model to factorization.

- Prime Sieve and Factorization Using Multiplication Table. Jongsoo Park; Cheong Youn // Journal of Mathematics Research;Jun2012, Vol. 4 Issue 3, p7
Using the properties of the table sieve, we can determine whether all given number, positive integer G, is a prime and whether it is possible to factor it out.

- Students Ask the Darnedest Things. // New York State Mathematics Teachers' Journal;2008, Vol. 58 Issue 2, p59
The article explains a mathematical question that teachers often hear students ask. Robert Rogers and Jamar Pickreign of the State University of New York (SUNY) at Fredonia explain why the number 1 is neither prime nor composite but is called a unit. According to Rogers, number 1 is a unit as...

- Triples of primes in arithmetic progressions. ELSHOLTZ, CHRISTIAN // Quarterly Journal of Mathematics;Dec2002, Vol. 53 Issue 4, p393
We show that there exist sets of primes A, B ? P n [1, N] with |A| = s, |B| = t such that all ï¿½ (ai + bj) are also prime, and where s = 0.33t N/(log N)t+1 holds, for sufficiently large N.

- Huaï¿½s theorem with s almost equal prime variables. Qing Feng Sun; Heng Cai Tang // Acta Mathematica Sinica;Jul2009, Vol. 25 Issue 7, p1145
It is proved unconditionally that every sufficiently large positive integer satisfying some necessary congruence conditions can be represented as the sum of s almost equal k-th powers of prime numbers for 2 = k = 10 and s = 2 k + 1, which gives a short interval version of Huaï¿½s theorem.

- On prime numbers of special kind on short intervals. Mot’kina, N. // Mathematical Notes;May/Jun2006, Vol. 79 Issue 5/6, p848
Suppose that the Riemann hypothesis holds. Suppose that where c is a real number, 1 < c â‰¤ 2. We prove that, for H> N 1/2+10Îµ, Îµ > 0, the following asymptotic formula is valid: .

- Estimates of certain arithmetic sums related to the number of divisors. Mit�kin, D. // Mathematical Notes;Sep/Oct2006, Vol. 80 Issue 3/4, p449
The article primarily presents the estimates of certain arithmetic sums in relation to the number of divisors. The article discusses various theorems on the inequalities of natural numbers, their proofs and corollary. The mathematical notes for the theorems discussed along with the remarks is...

- A refined bound for sum-free sets in groups of prime order. Deshouillers, Jean-Marc; Lev, Vsevolod F. // Bulletin of the London Mathematical Society;Oct2008, Vol. 40 Issue 5, p863
Improving upon earlier results of Freiman and the present authors, we show that if p is a sufficiently large prime and A is a sum-free subset of the group of order p, such that n: = |A| > 0.318p, then A is contained in a dilation of the interval [n, p âˆ’n] (mod p).