Primes and Twin Primes Generator Algorithms

Note on the cardinality difference between primes and twin primes and its impact on function x/ln(x) in prime number theorem

10.1063/1.5044134 ◽

2018 ◽

Cited By ~ 3

Author(s):

Sandor Kristyan

Keyword(s):

Prime Number ◽

Prime Number Theorem ◽

Twin Primes

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Some Families of Designs for Multistage Experiments: Mutually Balanced Youden Designs when the Number of Treatments is Prime Power or Twin Primes. I

The Annals of Mathematical Statistics ◽

10.1214/aoms/1177692384 ◽

1972 ◽

Vol 43 (5) ◽

pp. 1517-1527 ◽

Cited By ~ 7

Author(s):

A. Hedayat ◽

E. Seiden ◽

W. T. Federer

Keyword(s):

Prime Power ◽

Twin Primes

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An original abstract over the twin primes, the Goldbach conjecture, the friendly numbers, the perfect numbers, the Mersenne composite numbers, and the Sophie Germain primes

Journal of Discrete Mathematical Sciences and Cryptography ◽

10.1080/09720529.2008.10698400 ◽

2008 ◽

Vol 11 (6) ◽

pp. 715-726 ◽

Cited By ~ 2

Author(s):

Ikorong Anouk Gilbert Nemron

Keyword(s):

Twin Primes ◽

Perfect Numbers

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A Property of Twin Primes

Integers ◽

10.1515/integers-2011-0121 ◽

2012 ◽

Vol 12 (4) ◽

Cited By ~ 1

Author(s):

Christian Aebi ◽

Grant Cairns

Keyword(s):

Twin Primes ◽

Quadratic Residues

Abstract.We determine the product of the invertible quadratic residues in

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Magic squares of squares over a finite field

Topology, Geometry, and Dynamics - Contemporary Mathematics ◽

10.1090/conm/773/15536 ◽

2021 ◽

pp. 111-122

Author(s):

Stewart Hengeveld ◽

Giancarlo Labruna ◽

Aihua Li

Keyword(s):

Finite Field ◽

Prime Numbers ◽

Similar Question ◽

Magic Squares ◽

Content Type ◽

Magic Square ◽

Twin Primes ◽

Quadratic Residues ◽

Perfect Squares ◽

Open Question

A magic square M M over an integral domain D D is a 3 × 3 3\times 3 matrix with entries from D D such that the elements from each row, column, and diagonal add to the same sum. If all the entries in M M are perfect squares in D D , we call M M a magic square of squares over D D . In 1984, Martin LaBar raised an open question: “Is there a magic square of squares over the ring Z \mathbb {Z} of the integers which has all the nine entries distinct?” We approach to answering a similar question when D D is a finite field. We claim that for any odd prime p p , a magic square over Z p \mathbb Z_p can only hold an odd number of distinct entries. Corresponding to LaBar’s question, we show that there are infinitely many prime numbers p p such that, over Z p \mathbb Z_p , magic squares of squares with nine distinct elements exist. In addition, if p ≡ 1 ( mod 120 ) p\equiv 1\pmod {120} , there exist magic squares of squares over Z p \mathbb Z_p that have exactly 3, 5, 7, or 9 distinct entries respectively. We construct magic squares of squares using triples of consecutive quadratic residues derived from twin primes.

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