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Journal articles on the topic 'Twin primes'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Zhou, Mi. "The twin primes' infinite rule." Advances in Engineering Technology Research 1, no. 1 (2022): 186. http://dx.doi.org/10.56028/aetr.1.1.186.

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In this paper, the rule of infinite twin primes is found. Generally speaking, the superposition of twin primes produces a third pair. A pair of twin primes plus a pair of twin primes produces a third pair, Starting with the third pair of twin prime pairs, for each pair of twin prime pairs, two pairs of twin prime pairs can always be found in the preceding pair, such that their sum is equal to the sum of this pair of twin prime pairs; Or from the second pair of twin primes (an,bn), at least one pair of twin primes can always be found in front of it, such that their sum is equal to the sum of so

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2

Wong, Bertrand. "The twin primes*." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 40e, no. 1 (2021): 75–86. http://dx.doi.org/10.5958/2320-3226.2021.00008.4.

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3

Iovane, Gerardo, Patrizia Di Gironimo, Elmo Benedetto, and Vittorio D’Alfonso. "Some Properties and Algorithms for Twin Primes." Applied Sciences 14, no. 17 (2024): 7902. http://dx.doi.org/10.3390/app14177902.

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In this article, we study some new properties of twin primes and algorithms for their generation. We find the necessary conditions to generate a pair of twins. These conditions seem to indicate that the conjecture is true, namely, there are infinitely many twin primes. Furthermore, we developed some algorithms that are very useful from a computer science point of view, which can be applied in cryptography and data encryption.

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4

MacKinnon, Nick, and Stephen M. Gagola. "Fibonacci Twin Primes: 10844." American Mathematical Monthly 109, no. 1 (2002): 78. http://dx.doi.org/10.2307/2695779.

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5

Wong, Bertrand. "On the twin primes*." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 40e, no. 2 (2021): 149–54. http://dx.doi.org/10.5958/2320-3226.2021.00021.7.

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6

Parady, B. K., Joel F. Smith, and Sergio E. Zarantonello. "Largest known twin primes." Mathematics of Computation 55, no. 191 (1990): 381. http://dx.doi.org/10.1090/s0025-5718-1990-1023767-2.

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7

Indlekofer, Karl-Heinz, and Antal Járai. "Largest known twin primes." Mathematics of Computation 65, no. 213 (1996): 427–29. http://dx.doi.org/10.1090/s0025-5718-96-00666-7.

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8

Harris, David. "Science visualized: Twin primes." Science News 184, no. 8 (2013): 38. http://dx.doi.org/10.1002/scin.5591840822.

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9

Segal, Nancy L. "Reared-Apart Chinese Twins: Chance Discovery/Twin-Based Research: Twin Study of Media Use; Twin Relations Over the Life Span; Breast-Feeding Opposite-Sex Twins/Print and Online Media: Twins in Fashion; Second Twin Pair Born to Tennis Star; Twin Primes; Twin Pandas." Twin Research and Human Genetics 20, no. 2 (2017): 180–85. http://dx.doi.org/10.1017/thg.2017.9.

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A January 2017 reunion of 10-year-old reared-apart Chinese twin girls was captured live on ABC's morning talk show Good Morning America, and rebroadcast on their evening news program Nightline. The twins’ similarities and differences, and their participation in ongoing research will be described. This story is followed by reviews of twin research concerning genetic and environmental influences on media use, twin relations across the lifespan and the breast-feeding of opposite-sex twins. Popular interest items include twins in fashion, the second twin pair born to an internationally renowned te

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10

Gueye, Ibrahima. "Conjecture in Additive Twin Primes Numbers Theory." Bulletin of Society for Mathematical Services and Standards 5 (March 2013): 27–30. http://dx.doi.org/10.18052/www.scipress.com/bsmass.5.27.

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For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. For the record, the theorem of Clement has quickly been known to be ineffective in the development of twin primes because of the factorial. This is why I thought ofusing the additive theory of numbers to find pairs of twin primes from the first two pairs of twin primes. What I have formulated as a conjecture. In same time i presentmy idea about the solution of the

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11

Matomäki, Kaisa, and Xuancheng Shao. "Vinogradov’s three primes theorem with almost twin primes." Compositio Mathematica 153, no. 6 (2017): 1220–56. http://dx.doi.org/10.1112/s0010437x17007072.

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In this paper we prove two results concerning Vinogradov’s three primes theorem with primes that can be called almost twin primes. First, for any $m$, every sufficiently large odd integer $N$ can be written as a sum of three primes $p_{1},p_{2}$ and $p_{3}$ such that, for each $i\in \{1,2,3\}$, the interval $[p_{i},p_{i}+H]$ contains at least $m$ primes, for some $H=H(m)$. Second, every sufficiently large integer $N\equiv 3~(\text{mod}~6)$ can be written as a sum of three primes $p_{1},p_{2}$ and $p_{3}$ such that, for each $i\in \{1,2,3\}$, $p_{i}+2$ has at most two prime factors.

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12

Indlekofer, Karl-Heinz, and Antal Járai. "Largest known twin primes and Sophie Germain primes." Mathematics of Computation 68, no. 227 (1999): 1317–25. http://dx.doi.org/10.1090/s0025-5718-99-01079-0.

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13

Gueye, Ibrahima. "Polynomial Characterization of Twin Primes in Function of another Prime." Bulletin of Society for Mathematical Services and Standards 5 (March 2013): 37–39. http://dx.doi.org/10.18052/www.scipress.com/bsmass.5.37.

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For two millennia, the prime numbers have continued to fascinatemathematicians. Indeed, a conjecture which dates back to this period states that thenumber of twin primes is infinite. In 1949 Clement showed a theorem on twin primesIn this paper I give the proof of a polynomial characterization of twin primes usingadditive primes number theory.

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14

Gueye, Ibrahima. "Twin Primes and Sophie Germain’s Prime Numbers." Bulletin of Society for Mathematical Services and Standards 6 (June 2013): 1–3. http://dx.doi.org/10.18052/www.scipress.com/bsmass.6.1.

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For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. In a recent article, I prooved a corollary of Clement’s theorem [1]. In this paper, I will proove shortly the link between twin primes and Sophie Germain’s prime numbers.

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15

Baibekov, S. N., and A. A. Durmagambetov. "Infinite Number of Twin Primes." Advances in Pure Mathematics 06, no. 13 (2016): 954–71. http://dx.doi.org/10.4236/apm.2016.613073.

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16

Friedlander, John B., and Henryk Iwaniec. "Twin primes via exceptional characters." Banach Center Publications 118 (2019): 95–105. http://dx.doi.org/10.4064/bc118-5.

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17

MacHale, Des, and Joseph Manning. "97.18 Variatins on twin primes." Mathematical Gazette 97, no. 539 (2013): 265–68. http://dx.doi.org/10.1017/s0025557200005866.

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18

Gueye, Ibrahima. "Twin Prime Numbers and Diophantine Equations." Bulletin of Society for Mathematical Services and Standards 5 (March 2013): 10–13. http://dx.doi.org/10.18052/www.scipress.com/bsmass.5.10.

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For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. Starting from Wilson's theorem, Clement’s theorem and the corollary of Clement’s theorem [1], I came to find Diophantine equations whose solution could lead to theproof of the infinitude of twin primes.

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19

Mercedes, Orús–Lacort, Orús Román, and Christophe Jouis Christophe Joui. "Analyzing twin primes, Goldbach's strong conjecture and Polignac's conjecture." Annals of Mathematics and Physics 7, no. 1 (2024): 076–84. http://dx.doi.org/10.17352/amp.000110.

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Here we analyze three well-known conjectures: (i) the existence of infinitely many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of Goldbach's strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac's conjecture. Our first step is an analysis of the existence of infinitely many twin prime nu

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20

Werner, Hürlimann. "First Digit Counting Compatibility II: Twin Prime Powers." Journal of Progressive Research in Mathematics 9, no. 1 (2016): 1341–47. https://doi.org/10.5281/zenodo.3976764.

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The first digits of twin primes follow a generalized Benford law with size-dependent exponent and tend to be uniformly distributed, at least over the finite range of twin primes up to 10^m, m=5,...,16. The extension to twin prime powers for a fixed power exponent is considered. Assuming the Hardy-Littlewood conjecture on the asymptotic distribution of twin primes, it is claimed that the first digits of twin prime powers associated to any fixed power exponent converge asymptotically to a generalized Benford law with inverse power exponent. In particular, the sequences of twin prime power first

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21

Jabari, Zakiya. "On The Infinity of Twin Primes and other K-tuples." International Journal of Mathematics and Computer Research 13, no. 01 (2025): 4739–61. https://doi.org/10.5281/zenodo.14631763.

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The paper uses the structure and math of Prime Generator Theory to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.

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22

Diouf, Madieyna. "On the distribution of twin primes." International Journal of Contemporary Mathematical Sciences 16, no. 4 (2021): 173–86. http://dx.doi.org/10.12988/ijcms.2021.91634.

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23

Conrey, Brian, and Jonathan P. Keating. "Pair correlation and twin primes revisited." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2194 (2016): 20160548. http://dx.doi.org/10.1098/rspa.2016.0548.

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We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.

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24

Ram Murty, M., and Akshaa Vatwani. "Twin primes and the parity problem." Journal of Number Theory 180 (November 2017): 643–59. http://dx.doi.org/10.1016/j.jnt.2017.05.011.

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25

Forbes, Tony. "A large pair of twin primes." Mathematics of Computation 66, no. 217 (1997): 451–56. http://dx.doi.org/10.1090/s0025-5718-97-00793-x.

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26

Garcia, Stephan Ramon, Elvis Kahoro, and Florian Luca. "Primitive Root Bias for Twin Primes." Experimental Mathematics 28, no. 2 (2017): 151–60. http://dx.doi.org/10.1080/10586458.2017.1360809.

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27

Guedes, Edigles, Raja Rama Gandhi, and Srinivas Kishan Anapu. "Are there Infinitely many Twin Primes?" Bulletin of Mathematical Sciences and Applications 5 (August 2013): 22–26. http://dx.doi.org/10.18052/www.scipress.com/bmsa.5.22.

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28

Yogananda, C. S. "Twin primes and the Pentium chip." Resonance 8, no. 3 (2003): 32. http://dx.doi.org/10.1007/bf02835803.

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29

Aiazzi, Bruno, Stefano Baronti, Leonardo Santurri, and Massimo Selva. "An Investigation on the Prime and Twin Prime Number Functions by Periodical Binary Sequences and Symmetrical Runs in a Modified Sieve Procedure." Symmetry 11, no. 6 (2019): 775. http://dx.doi.org/10.3390/sym11060775.

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In this work, the Sieve of Eratosthenes procedure (in the following named Sieve procedure) is approached by a novel point of view, which is able to give a justification of the Prime Number Theorem (P.N.T.). Moreover, an extension of this procedure to the case of twin primes is formulated. The proposed investigation, which is named Limited INtervals into PEriodical Sequences (LINPES) relies on a set of binary periodical sequences that are evaluated in limited intervals of the prime characteristic function. These sequences are built by considering the ensemble of deleted (that is, 0) and undelet

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30

Di Pietro, Gabriele. "Numerical analysis approach to twin primes conjecture." Notes on Number Theory and Discrete Mathematics 30, no. 3 (2024): 580–86. http://dx.doi.org/10.7546/nntdm.2024.30.3.580-586.

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This paper provides a better approximation of the functions presented in the article “Numerical Analysis Approach to Twin Primes Conjecture” (see [3]). The new estimates highlight the approximations used in the previous article and the validity of Theorems 1 and 2 through the use of the false hypothesis based on the distribution of primes punctually following the Logarithmic Integral Li(x) (see [4] and [7], pp. 174–176) will be re-evaluated.

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31

Belovas, Igoris, Martynas Sabaliauskas, and Paulius Mykolaitis. "Apie sveikųjų skaičių sekų, asocijuotų su pirminiais dvyniais, apskaičiavimą." Lietuvos matematikos rinkinys 64 (November 20, 2023): 23–29. http://dx.doi.org/10.15388/lmr.2023.33586.

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The twin primes conjecture states that there are infinitely many twin primes. While studying this hypothesis, many important results were obtained, but the problem remains unsolved. In this work, the problem is studied from the side of experimental mathematics. Using the probabilistic Miller–Rabin primality test and parallel computing technologies, the distribution of prime pairs in the intervals (2n; 2n+1] is studied experimentally.

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32

Forbes, Tony. "79.62 A Large Pair of Twin Primes." Mathematical Gazette 79, no. 486 (1995): 577. http://dx.doi.org/10.2307/3618102.

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33

Dilcher, Karl, and Kenneth B. Stolarsky. "A Pascal-Type Triangle Characterizing Twin Primes." American Mathematical Monthly 112, no. 8 (2005): 673. http://dx.doi.org/10.2307/30037570.

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34

Di Pietro, Gabriele. "Numerical analysis approach to twin primes conjecture." Notes on Number Theory and Discrete Mathematics 27, no. 3 (2021): 175–83. http://dx.doi.org/10.7546/nntdm.2021.27.3.175-183.

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The purpose of this paper is to demonstrate how the modified Sieve of Eratosthenes is used to have an approach to twin prime conjecture. If the Sieve is used in its basic form, it does not produce anything new. If it is used through the numerical analysis method explained in this paper, we obtain a specific counting of twin primes. This counting is based on the false assumption that distribution of primes follows punctually the Logarithmic Integral function denoted as Li(x) (see [5] and [10], pp. 174–176). It may be a starting point for future research based on this numerical analysis method t

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35

Dilcher, Karl, and Kenneth B. Stolarsky. "A Pascal-Type Triangle Characterizing Twin Primes." American Mathematical Monthly 112, no. 8 (2005): 673–81. http://dx.doi.org/10.1080/00029890.2005.11920240.

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36

Korevaar, Jacob. "Distributional Wiener-Ikehara theorem and twin primes." Indagationes Mathematicae 16, no. 1 (2005): 37–49. http://dx.doi.org/10.1016/s0019-3577(05)80013-8.

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37

Benedetto, E. "Arithmetical approach to the twin primes conjecture." ANNALI DELL'UNIVERSITA' DI FERRARA 57, no. 1 (2009): 191–98. http://dx.doi.org/10.1007/s11565-009-0070-8.

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38

Cohen, Joel E. "Statistics of Primes (and Probably Twin Primes) Satisfy Taylor's Law from Ecology." American Statistician 70, no. 4 (2016): 399–404. http://dx.doi.org/10.1080/00031305.2016.1173591.

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39

Kharaghani, Hadi, and Sho Suda. "Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes." Finite Fields and Their Applications 63 (March 2020): 101631. http://dx.doi.org/10.1016/j.ffa.2019.101631.

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40

Goldston, D. A., and C. Y. Yildirim. "Primes in Short Segments of Arithmetic Progressions." Canadian Journal of Mathematics 50, no. 3 (1998): 563–80. http://dx.doi.org/10.4153/cjm-1998-031-9.

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AbstractConsider the variance for the number of primes that are both in the interval [y,y + h] for y ∈ [x,2x] and in an arithmetic progression of modulus q. We study the total variance obtained by adding these variances over all the reduced residue classes modulo q. Assuming a strong form of the twin prime conjecture and the Riemann Hypothesis one can obtain an asymptotic formula for the total variance in the range when 1 ≤ h/q ≤ x1/2-∈ , for any ∈ > 0. We show that one can still obtain some weaker asymptotic results assuming the Generalized Riemann Hypothesis (GRH) in place of the twin pri

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41

Ascarelli, Paolo. "Detection and Rarefaction of the Twin Primes Numbers." European Journal of Mathematics and Statistics 4, no. 2 (2023): 36–37. http://dx.doi.org/10.24018/ejmath.2023.4.2.216.

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In this manuscript are considered 3 types of numbers: a) integral numbers like for example (x)=10^10 b) prime numbers whose properties is to be only divisible by themselves c) twin numbers The number of twin primes contained under the number (x) is here derived by: 1) a mathematical function proposed by Gauss (1792-1796) based on a converging logarithmic sum, 2) Euclid’s theorems on prime numbers.

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42

Gueye, Ibrahima. "Approching the Twin Prime Constant." Bulletin of Society for Mathematical Services and Standards 2 (June 2012): 70–73. http://dx.doi.org/10.18052/www.scipress.com/bsmass.2.70.

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43

Kowitz, Krzysztof. "Twin, cousin, and sexy prime counting function. Explicit formulas." Ukrains’kyi Matematychnyi Zhurnal 76, no. 8 (2024): 1260–64. http://dx.doi.org/10.3842/umzh.v76i8.7567.

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UDC 511 We give explicit formulas for the twin-prime and cousin-prime counting functions. We propose a formula that computes the number of primes less than or equal to n whose difference is m ⩾ 6. We also present a characterization specifying when two numbers whose difference is n ⩾ 2 are primes.

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44

Dence, Joseph B., and Thomas P. Dence. "A Necessary and Sufficient Condition for Twin Primes." Missouri Journal of Mathematical Sciences 7, no. 3 (1995): 129–31. http://dx.doi.org/10.35834/1995/0703129.

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45

Dinculescu, A. "The Twin Primes Seen from a Different Perspective." British Journal of Mathematics & Computer Science 3, no. 4 (2013): 691–98. http://dx.doi.org/10.9734/bjmcs/2013/4358.

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46

Yue, Zhang. "A Proof on the Conjecture of Twin Primes." International Journal of Applied Mathematics and Theoretical Physics 5, no. 3 (2019): 82. http://dx.doi.org/10.11648/j.ijamtp.20190503.15.

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47

Baier, Stephan. "An Elementary Approach to the Twin Primes Problem." Monatshefte f�r Mathematik 143, no. 4 (2004): 269–83. http://dx.doi.org/10.1007/s00605-004-0270-3.

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48

Gocgen, Ahmet F. "Gocgen Approach for Zeta Function in Twin Primes." International Journal of Pure and Applied Mathematics Research 4, no. 1 (2024): 28–33. http://dx.doi.org/10.51483/ijpamr.4.1.2024.28-33.

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49

Chillali, Abdelhakim. "R-prime numbers of degree k." Boletim da Sociedade Paranaense de Matemática 38, no. 2 (2018): 75–82. http://dx.doi.org/10.5269/bspm.v38i2.38218.

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In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient of a function for it to be called one-way (see Theoretical Definition, in article). A twin prime is a prime number that has a prime gap of two, in other words, differs from another prime number by two, for example the twin prime pair (5,3). The question o

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50

SUN, ZHI-WEI. "ON A SEQUENCE INVOLVING SUMS OF PRIMES." Bulletin of the Australian Mathematical Society 88, no. 2 (2013): 197–205. http://dx.doi.org/10.1017/s0004972712000986.

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AbstractFor $n= 1, 2, 3, \ldots $ let ${S}_{n} $ be the sum of the first $n$ primes. We mainly show that the sequence ${a}_{n} = \sqrt[n]{{S}_{n} / n}~(n= 1, 2, 3, \ldots )$ is strictly decreasing, and moreover the sequence ${a}_{n+ 1} / {a}_{n} ~(n= 10, 11, \ldots )$ is strictly increasing. We also formulate similar conjectures involving twin primes or partitions of integers.

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