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

Zoe's Design: A poster for Peter Cameron's 60th birthday, Ambleside, August 2007.

See also Theorem of the Day, Number 100.

Geometric Graph Designs: Slides for BCC 2011 talk, Exeter, July 2011.

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.

[with T. S. Griggs and K. A. Forbes], Completing the design spectra for graphs with six vertices and eight edges, *Australas. J. Combin.* **70** (2018), 386-389.

[with T. S. Griggs], Designs for graphs with six vertices and nine edges, *Australas. J. Combin.* **70** (2018), 52-74
.

[with T. S. Griggs and T. J. Forbes], Theta Graph Designs, *J. Algorithms and Computation* **49** issue 1 (2017) 1-16; http://arxiv.org/abs/1703.01483.

[with T. S. Griggs and T. J. Forbes], Archimedean graph designs - II, *Discrete Math.* **340** (2017) 1598-1611.

Designs for 24-vertex snarks, *Utilitas Math.*, accepted, 2016; http://arxiv.org/abs/1607.04847.

[with T. J. Forbes], Hanoi revisited, *Math. Gazette* **100** (November 2016), 435-441.

Snark designs, *Utilitas Math.*, accepted, 2015; https://arxiv.org/abs/1207.3032v2

[with T. S. Griggs, C. Psomas and J. Širáň]. Biembeddings of Steiner triple systems in
orientable pseudosurfaces with one pinch point,
*Glasgow Mathematical Journal*, **56** (2), (May 2014), 251-260.

[with T. S. Griggs], Icosahedron designs, *Australas. J. Combin.*, **52** (2012), 215-228.

[with T. S. Griggs], Archimedean graph designs, *Discrete Math.*, **313** (2013) 1138-1149.

[with P. Adams, D. E. Bryant and T. S. Griggs], Decomposing the complete graph into dodecahedra, *J. Statistical Planning and Inference* **142** (2012), 1040-1046.

[with T. S. Griggs and F. C. Holroyd], Truncated Tetrahedron, Octahedron and Cube Designs,
*J. Combinatorial Mathematics and Combinatorial Computing*, **80** (2012), 95-111.

[with C. J. Colbourn, M. J. Grannell, T. S. Griggs, P. Kaski, P. R. J. Östergård, D. A. Pike, and O. Pottonen], Properties of the Steiner Triple Systems of Order 19,
*Electronic Journal of Combinatorics*, 17(1), 2010, R98, 30pp.

Eleven Billion STS(19)s: Slides for talks given at PCC, Warwick, June 2009, and at LSBU, September 2009.

[with T. S. Griggs and F.C. Holroyd], Rhombicuboctahedron designs,
*J. Combinatorial Mathematics and Combinatorial Computing*, **75** (2010), 161-165.

[with M. J. Grannell and T. S. Griggs], Further 6-sparse Steiner triple systems,
*Graphs and Combinatorics* **25** (2009), 49-64.

[with M. J. Grannell, T. S. Griggs and R. G. Stanton], On the small covering numbers *g*_{1}^{(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 Journal of 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.

Three Primes: Notes for talks given at London South Bank University, February 2012.

Congruence Properties of the Partition Function: Notes for talks given at London South Bank University, 24 September, 8 October and 19 November 2008.

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)

Gigantic prime triplets,
*M500* **226** (February 2009)

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.

⇒ Theorem of the Day Number 109,
The Beardwood-Halton-Hammersley Theorem.

⇒ 2009 Calendar: 12 Theorems by Women Mathematicians.

And there's Manfred Toplic's site at
The Nine and Ten Primes Project.

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.

A large pair of twin primes,
*Math. Comp.* **66** (1997), 451-455.

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