# Pocklington's Theorem and Bertrand's Postulate

Formalized Mathematics (2006)

- Volume: 14, Issue: 2, page 47-52
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topMarco Riccardi. "Pocklington's Theorem and Bertrand's Postulate." Formalized Mathematics 14.2 (2006): 47-52. <http://eudml.org/doc/267204>.

@article{MarcoRiccardi2006,

abstract = {The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.},

author = {Marco Riccardi},

journal = {Formalized Mathematics},

language = {eng},

number = {2},

pages = {47-52},

title = {Pocklington's Theorem and Bertrand's Postulate},

url = {http://eudml.org/doc/267204},

volume = {14},

year = {2006},

}

TY - JOUR

AU - Marco Riccardi

TI - Pocklington's Theorem and Bertrand's Postulate

JO - Formalized Mathematics

PY - 2006

VL - 14

IS - 2

SP - 47

EP - 52

AB - The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.

LA - eng

UR - http://eudml.org/doc/267204

ER -

## References

top- [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
- [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [5] Grzegorz Bancerek. Joining of decorated trees. Formalized Mathematics, 4(1):77-82, 1993.
- [6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [7] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
- [8] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
- [9] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
- [10] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [11] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [12] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [13] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
- [14] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- [15] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4):573-577, 1997.
- [16] Artur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179-186, 2004.
- [17] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
- [18] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.
- [19] W. J. LeVeque. Fundamentals of Number Theory. Dover Publication, New York, 1996. Zbl1141.11300
- [20] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
- [21] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.
- [22] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
- [23] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.
- [24] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
- [25] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
- [26] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
- [27] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
- [28] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- [29] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.
- [30] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
- [31] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
- [1] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004. Zbl1098.00001
- [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

## NotesEmbed ?

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