Tony Forbes

http://anthony.d.forbes.googlepages.com/adf.htm

Sudoku puzzles

Week 149: Monday 21 July 2008

Easy sudoku puzzle
Harder sudoku puzzle
Harder sudoku puzzle
Hard sudoku puzzle
Hard sudoku puzzle
Easier quasi-magic sudoku puzzle ⇒ [solution]
Harder quasi-magic sudoku puzzle ⇒ [solution]
16 x 16 sudoku puzzle ⇒ [solution]
More puzzles

Research interests

E-mail me at anthony.d.forbes@gmail.com for items not available online.

The largest known prime k-tuplets

MM61 project[progress]

Combinatorics

Zoe's Design: A poster for Peter Cameron's 60th birthday, Ambleside, August 2007.
See also Theorem of the Day, number 100.

Applications of Weil's Theorem on Character Sums: Notes for a talk given at London South Bank University, 7 September 2007.

Configurations and colouring problems in block designs, Ph.D. thesis, The Open University, November 2006.
Abstract.
The Thesis. Please e-mail me to say so if you download it. - Thanks.

Steiner triple system configuration data: 6 blocks : 7 blocks : 8 blocks : 9 blocks : Tradeable : Dense.

A collection of small triple systems.

Combinatorics papers

[with M. J. Grannell, T. S. Griggs and R. G. Stanton], On the small covering numbers g1(5)(v), Utilitas Mathematica 74 (2007), 77-96.

[with M. J. Grannell and T. S. Griggs], New type-B colorable S(2,4,v) designs, J. Combin. Designs 15 (2007), 357-368.

[with M. J. Grannell and T. S. Griggs], The Design of the Century, Mathematica Slovaca 57 (2007) No. 5, 495-499.
See also Theorem of the Day, number 100.

[with M. J. Grannell and T. S. Griggs], On 6-sparse Steiner triple systems, J. Combin. Theory, Series A 114 (2007), 235-252.

[with M. J. Grannell and T. S. Griggs], Distance and fractional isomorphism in Steiner triple systems, Rendiconti del Circolo Matematico di Palermo, Series II LVI (2007), 17-32.

[with M. J. Grannell and T. S. Griggs], Steiner triple systems and existentially closed graphs, Electronic J. Combinatorics 12 (2005), #R42.

[with M. J. Grannell and T. S. Griggs], On independent sets, Mathematica Slovaca 55 No. 4 (2005), 375-377.

[with M. J. Grannell and T. S. Griggs], Independent sets in Steiner triple systems, Ars Combinatoria 72 (2004) 161-169.

[with M. J. Grannell and T. S. Griggs], Configurations and trades in Steiner triple systems, The Australasian Journal of Combinatorics 29 (2004), 75-84.

Uniquely 3-colourable Steiner triple systems, J. Combin. Theory, Series A 101 (2003), 49-68.

[with M. J. Grannell and T. S. Griggs], On colourings of Steiner triple systems, Discrete Mathematics 261 (2003), 255-276.

Number theory

Factorization of Integers: Notes for talks given at London South Bank University, 20 February and 19 March 2008.

Elliptic curves, Factorization and Primality Testing: Notes for talks given at London South Bank University, 7, 14 and 21 November 2007.

Titanic prime quintuplets, M500 189 (December 2002)

Large prime quadruplets, Mathematical Gazette 84 no. 501 (November 2000), 447-452

Ten consecutive primes in arithmetic progression

Two hundred and fourteen primes in the vicinity of P = 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004 18036 03417 75890 43417 03348 88215 90672 29719. Ten consecutive primes in arithmetic progression appear in a vertical line. The top one is P. The other nine are P + 210, P + 420, ..., P + 1890. See also:
Theorem of the Day Number 32, The Green-Tao Theorem on Primes in Arithmetic Progression, and
Theorem of the Day Number 109, The Beardwood-Halton-Hammersley Theorem.

VFYPR : A PC program for verifying primes

Number theory papers

Fifteen consecutive integers with exactly four prime factors, Math. Comp. 71 (2002), 449-452.

[with H. Dubner, N. Lygeros, M. Mizony, H. Nelson and P. Zimmermann], Ten Consecutive Primes in Arithmetic Progression, Math. Comp. 71 (2002), 1323-1328. Also available as a PDF file.

[with Harvey Dubner], Prime Pythagorean triangles, J. Integer Sequences 4 (2001), Article 01.2.3

Prime clusters and Cunningham chains, Math. Comp. 68 (1999), 1739-1747.

Congruence properties of functions related to the partition function, Pacific Journal of Mathematics 158 (1993), 145-156.

Other stuff

Quasi-magic sudoku puzzles, M500 215 (April 2007), 1-10.

Rubik's Cube, Rubik's Revenge and Rubik's 5x5x5 cube.