# More on Divisibility Criteria for Selected Primes

Adam Naumowicz; Radosław Piliszek

Formalized Mathematics (2013)

- Volume: 21, Issue: 2, page 87-94
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topAdam Naumowicz, and Radosław Piliszek. "More on Divisibility Criteria for Selected Primes." Formalized Mathematics 21.2 (2013): 87-94. <http://eudml.org/doc/266853>.

@article{AdamNaumowicz2013,

abstract = {This paper is a continuation of [19], where the divisibility criteria for initial prime numbers based on their representation in the decimal system were formalized. In the current paper we consider all primes up to 101 to demonstrate the method presented in [7].},

author = {Adam Naumowicz, Radosław Piliszek},

journal = {Formalized Mathematics},

keywords = {divisibility; divisibility rules; decimal digits},

language = {eng},

number = {2},

pages = {87-94},

title = {More on Divisibility Criteria for Selected Primes},

url = {http://eudml.org/doc/266853},

volume = {21},

year = {2013},

}

TY - JOUR

AU - Adam Naumowicz

AU - Radosław Piliszek

TI - More on Divisibility Criteria for Selected Primes

JO - Formalized Mathematics

PY - 2013

VL - 21

IS - 2

SP - 87

EP - 94

AB - This paper is a continuation of [19], where the divisibility criteria for initial prime numbers based on their representation in the decimal system were formalized. In the current paper we consider all primes up to 101 to demonstrate the method presented in [7].

LA - eng

KW - divisibility; divisibility rules; decimal digits

UR - http://eudml.org/doc/266853

ER -

## References

top- [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
- [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
- [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [4] Grzegorz Bancerek. Sequences of ordinal numbers. Formalized Mathematics, 1(2):281-290, 1990.
- [5] Grzegorz Bancerek. Increasing and continuous ordinal sequences. Formalized Mathematics, 1(4):711-714, 1990.
- [6] Grzegorz Bancerek. Veblen hierarchy. Formalized Mathematics, 19(2):83-92, 2011. doi:10.2478/v10037-011-0014-5.[Crossref] Zbl1276.03044
- [7] C.C. Briggs. Simple divisibility rules for the 1st 1000 prime numbers. arXiv preprint arXiv:math/0001012, 2000.
- [8] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
- [9] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [10] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [11] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- [13] Krzysztof Hryniewiecki. Recursive definitions. Formalized Mathematics, 1(2):321-328, 1990.
- [14] Magdalena Jastrz¸ebska and Adam Grabowski. Some properties of Fibonacci numbers. Formalized Mathematics, 12(3):307-313, 2004.
- [15] Artur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181-187, 2005.
- [16] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
- [17] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.
- [18] Yatsuka Nakamura and Hisashi Ito. Basic properties and concept of selected subsequence of zero based finite sequences. Formalized Mathematics, 16(3):283-288, 2008. doi:10.2478/v10037-008-0034-y.[Crossref]
- [19] Adam Naumowicz. On the representation of natural numbers in positional numeral systems. Formalized Mathematics, 14(4):221-223, 2006. doi:10.2478/v10037-006-0025-9.[Crossref]
- [20] Karol Pak. Stirling numbers of the second kind. Formalized Mathematics, 13(2):337-345, 2005.
- [21] Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
- [22] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
- [23] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [25] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
- [26] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
- [27] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.