an expository essay">

Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 12 (2017), 229 -- 252

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This work is licensed under a Creative Commons Attribution 4.0 International License.

CONJECTURE OF TWIN PRIMES (STILL UNSOLVED PROBLEM IN NUMBER THEORY)
AN EXPOSITORY ESSAY

Hayat Rezgui

Abstract. The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called "Twin primes conjecture" (8th problem of David Hilbert, stated in 1900) which has eluded many gifted mathematicians. This conjecture has been circulating for decades, even with the progress of contemporary technology that puts the whole world within our reach. So, simple to state, yet so hard to prove. Basic Concepts, many and varied topics regarding the Twin prime conjecture will be cover.

2010 Mathematics Subject Classification: 11A41; 97Fxx; 11Yxx.
Keywords: Twin primes; Brun's constant; Zhang's discovery; Polymath project.

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Hayat Rezgui
Laboratory: E.D.P.N.L. and Department of Mathematics,
École Normale Supérieure,
B.P. 92, Vieux Kouba, 16308, Algiers, Algeria.
E-mail: rezguihayat@gmail.com

http://www.utgjiu.ro/math/sma