<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Skewes’ number was discovered in 1933 by South African mathematician Stanley Skewes as upper bound for the first sign change of the difference π (<italic>x</italic>) − li(<italic>x</italic>). Whether a Skewes’ number is an integer is an open problem of Number Theory. Assuming Schanuel’s conjecture, it can be shown that Skewes’ number is transcendental. In our paper we have chosen a different approach to prove Skewes’ number is an integer, using lattice points and tangent line. In the paper we acquaint the reader also with prime numbers and their use in RSA coding, we present the primary algorithms Lehmann test and Rabin-Miller test for determining the prime numbers, we introduce the Prime Number Theorem and define the prime-counting function and logarithmic integral function and show their relation.</p>
</abstract>

Skewes’ number was discovered in 1933 by South African mathematician Stanley Skewes as upper bound for the first sign change of the difference π (x) − li(x). Whether a Skewes’ number is an integer is an open problem of Number Theory. Assuming Schanuel’s conjecture, it can be shown that Skewes’ number is transcendental. In our paper we have chosen a different approach to prove Skewes’ number is an integer, using lattice points and tangent line. In the paper we acquaint the reader also with prime numbers and their use in RSA coding, we present the primary algorithms Lehmann test and Rabin-Miller test for determining the prime numbers, we introduce the Prime Number Theorem and define the prime-counting function and logarithmic integral function and show their relation.

Proof the Skewes’ number is not an integer using lattice points and tangent line

Constantine The Philosopher University in Nitra

Journal of Applied Mathematics, Statistics and Informatics

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

Skewes’ number was discovered in 1933 by South African mathematician Stanley Skewes as upper bound for the first sign change of the difference π (x) − li(x)....

Proof the Skewes’ number is not an integer using lattice points and tangent line

Published Online: Dec 30, 2021

Page range: 5 - 18

Received: Sep 01, 2021

DOI: https://doi.org/10.2478/jamsi-2021-0006

Keywords
Skewes’ number, proof, Prime Number Theorem, prime-counting function, logarithmic integral function, lattice points, tangent line

© 2021 V. Ďuriš et al., published by Sciendo

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

Proof the Skewes’ number is not an integer using lattice points and tangent line

Published Online: Dec 30, 2021

Page range: 5 - 18

Received: Sep 01, 2021

DOI: https://doi.org/10.2478/jamsi-2021-0006

KeywordsSkewes’ number, proof, Prime Number Theorem, prime-counting function, logarithmic integral function, lattice points, tangent line

© 2021 V. Ďuriš et al., published by Sciendo

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

Keywords
Skewes’ number, proof, Prime Number Theorem, prime-counting function, logarithmic integral function, lattice points, tangent line