Vollum Adjunct Professor of Science and

Director, Center for Advanced Computation, Reed College [1978-2012]

Prof. Richard E. Crandall.

Richard Crandall was also an Apple Distinguished Scientist, and had previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. In 1997 he founded a consulting firm, Perfectly Scientific, Inc., dedicated to industrial algorithm design. His primary interest was interdisciplinary scientific computation, though he also authored numerous theoretical papers in quantum physics, biology, mathematics, and chemistry, as well as various patents across engineering fields.

- Books
- Works in the field of physics
- Works in the fields of algorithms, mathematics, and computer science
- Works in the field of biology
- Media publications
- Publications for Apple's Advanced Computation Group
- Patents
- Awards and media recognition

Crandall, R. and Pomerance, C. 2001, *Prime numbers: A Computational Perspective*, Springer-Verlag

Levich, M. and Crandall, R. 1997, *A Network Orange*, Springer-Verlag

Crandall, R. 1996, *Topics in Advanced Scientific Computation*, Springer-Verlag

Crandall, R. 1994, *Projects in Scientific Computation*, Springer-Verlag

Crandall, R. 1991, *Mathematica for the Sciences*, Addison-Wesley, Reading, Mass.

Crandall, R. and Colgrove, M. M. 1986, *Scientific Programming with Macintosh Pascal*, John Wiley & Sons, New York

Crandall, R. 1983, *Pascal Applications for the Sciences*, John Wiley & Sons, New York

Crandall, R. E. 1999, "New representations for the Madelung constant," *Experimental Mathematics* 8:4, 367-379

Crandall, R. E. 1996, "On the quantum zeta function," *J. Phys. A: Math.* Gen. 29, 7 Nov., 6795-6816

Crandall, R. E. 1993, "Combinatorial approach to Feynman path integration," *J. Physics A: Math.* Gen., 26, 1993, 3627-3648

Powell, J. W. and Crandall, R. E. 1993, "Lattice dynamics for a simplified DNA model," *Mathematica in Education*, 2, 3, 15-20

Crandall, R.E. and Buhler J.P. 1990, "On the convergence problem for lattice sums," *J. Phys. A: Math.* Gen. 23, 2523-2528

Crandall, R.E. and Dunne, T.G. 1989, "Heuristic methods for counting and sizing of molecules in the liquid state." *Amer. Journ. Of Physics*, April, Vol. 57, No. 4, pp 346-351.

Crandall, R. E. and Buhler, J.P. 1987, "Elementary function expansions for Madelung constants," *J. Phys. A: Math.* Gen. 20, 5497-5510

Crandall, R. E. and Delord, J. F. 1987, "The potential within a crystal lattice," *J. Phys. A: Math.* Gen. 20, 2279-2292

Crandall, R. E., Bettega, R. and Whitnell, R. 1985, "A class of exactly soluble three-body problems," *J. Chem. Phys.* (September)

Crandall, R.E. and Wheeler, N.A. 1984, "Klein-Gordon radio and the problem of photon mass," *Il Nuovo Cimento*; Vol. 80 B, N.2 (April)

Crandall, R.E., Whitnell, R. and Bettega, R. 1984, "Exactly soluble two-electron atomic model," *Amer. Journ. Phys.* (May)

Crandall, R.E. and Delord, J. 1983, "Minimal apparatus for determination of Planck's Constant," *Amer. Journ. Phys.* (January)

Crandall, R.E. 1983, "Exact propagator for motion confined to a Sector," *J. Phys. A*, Vol. 16, No. 3 (February)

Crandall, R.E. 1983, "Electronic Cavendish Device," *Amer. Journ. Phys.* (May); this is abstract of 1981 Competition 1st Prize

Crandall, R. E. and Litt, B.R. 1983, "Reassembly and time advance in reflectionless scattering," *Ann. Phys.* 146, 2, 458

Crandall, R.E. 1983, "Fast eigenvalue algorithm for central potentials," *J. Phys. A*, 16, L395

Crandall, R.E. 1983, "Exact propagator for reflectionless potentials," *J. Phys. A: Math.* Gen. 16, 3005

Crandall, R.E. 1983, "Photon mass experiment," *Amer. Journ. Phys.* (August)

Crandall, R.E. 1980, "On the rings of Saturn," *J. Oregon Acad. Sci.*, (March)

Crandall, R.E. and Reno, M.H. 1982, "Ground state bounds for potentials x^{ν}," *J. Math. Phys.*, 23(1) (January)

Crandall, R.E. 1982, "Minimal apparatus for speed of light measurement," *Amer. Journ. Phys.* (December)

Crandall, R.E., Griffiths, D., Wheeler, N. and Mayer, R. 1982, "The fields of an infinite plane of color," *Phys. Rev.* D., 24

Crandall, R.E. and Wishnow, E.C. 1981, "Listening to the Doppler shift of visible light," *Amer. Journ. Phys.* (May)

D.H. Bailey, J. Borwein, and R. Crandall, "Advances in the theory of box integrals," manuscript, 30 March 2009

D. Borwein, J. Borwein, and R. Crandall, "Effective Laguerre asymptotics," manuscript, 28 May 2008

R. Crandall, "Theory of ROOF walks," manuscript, 26 March 2012

R. Crandall, "Note on sinc-kernel sums and Poisson transformation," manuscript, June 2007

D. Bailey, J. Borwein, and R. Crandall, "Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics," *Experimental Mathematics*, **18** (2009), 107-116.

D. Bailey, D. Borwein, J. Borwein, and R. Crandall, "Hypergeometric forms for Ising-class integrals," *Experimental Mathematics*, **16** (2007), 257-276.

D. Bailey, J. Borwein, and R. Crandall, "Box integrals," *Journal of Computational and Applied Mathematics* 206(2007) 196-208.

Published version: www.sciencedirect.com

D. Bailey, J. Borwein, and R. Crandall, "Integrals of the Ising class," *J. Physics A.: Math. Gen.* (to appear, 2007).

Crandall, R. E. "Note on fast polylogarithm computation," manuscript, January 2006

Crandall, R. E. "Fast evaluation of Zucker moment-sums," manuscript, September 2005

Crandall, R. E. "Fast evaluation of the Witten zeta function," manuscript, August 2005

Crandall, R. E. "On a Bessel-integral of J. Borwein, " manuscript, Aug 2004

Bedau, M., Crandall, R. E., and Raven, M. 2004, "Cryptographic hash functions based on Artificial Life," manuscript

D. Borwein, J. Borwein, R. Crandall, and R. Mayer, "On the dynamics of certain recurrence relations," *Ramanujan Journal* (Special issue for Richard Askey's 70th birthday), accepted July 2004.

Borwein, J., Crandall, R. and Fee, G. 2004, "On the Ramanujan AGM fraction. Part I: The real-parameter case", *Experimental Mathematics*, **13**, 275-286.

Borwein, J. and Crandall, R. 2004, "On the Ramanujan AGM fraction. Part II: The complex-parameter case", *Experimental Mathematics*, **13**, 287-296.

D. Bailey, J. Borwein, R. Crandall and C. Pomerance, "On the Binary Expansions of Algebraic Numbers," *Journal de Theorie des Nombres de Bordeaux*, vol. 16 (2004), pp. 487-518

Crandall, R., Mayer, E. and Papadopoulos, J. 2003, "The twenty-fourth Fermat Number is composite," *Math. Comp.* 72 1555-1572

Bailey, D. and Crandall, R. 2002, "Random generators and normal numbers," *Exp. Math.* Vol. 11, No. 4, 527-547

Bailey, D. and Crandall, R., 2000, "On the random character of fundamental constant expansions," *Exp. Math.* 10, 2001, 175-190

Crandall, R. 2000, "Algorithms for localized dart-throwing," Manuscript

Borwein, J., Bradley, D. and Crandall, R. 2000, "Computational strategies for the Riemann zeta function," *J. Comp. App. Math.*, 121, 247-296

Crandall, R.E. 2000, "Fast evaluation for a certain class of lattice sums"

Buhler, J., Crandall, R., Ernvall, R., Mets, T., and Shokrollahi, M. 2000, "Irregular primes and cyclotomic invariants to 12 million," *J. Symbolic Comput.* 11, 1-8

Brent, R. P. Crandall, R. E., Dilcher, K. and van Halewyn, C. 2000, "Three new factors of Fermat Numbers," *Math. Comp.* (July)

Crandall, R., Hofmann, U. and Lozes, R. 1999, "Contrast limitations in electron-beam lithography," *J. Vac. Sci. Technol.* B 17(6), 2945-2947

Hofmann, U., Crandall, R. and Johnson, L. 1999, "Fundamental performance of state-of the-art proximity effect correction methods," *J. Vac. Sci. Technol.* B 17(6) (Nov/Dec) 2940-2944

Crandall, R. E. 1999, "Parallelization of Pollard-rho factorization,"

Crandall, R. E. 1999, "Integer convolution via split-radix fast Galois transform," manuscript

Crandall, R. E. 1998, "Applications of space-filling curves," Manuscript

Crandall, R. E. 1998, "Fast evaluation of Epstein zeta functions," manuscript

Crandall, R. E. and Farrell, J. 1997, "Optimization of two dimensional real convolutions," manuscript

Crandall, R. E. 1997, "Floating-point convolutions of length 3 * 2^k," manuscript

Bailey, D., Borwein, J. and Crandall, R. 1997, "On the Khintchine Constant," *Math. Comp.*, 66, 217, 417-431

Crandall, R. E., Dilcher, K. and Pomerance, P. 1997, "A search for Wieferich and Wilson primes," *Math. Comp.*, 66, 217, 433-449

Crandall, R. 1996, "Fast evaluation of multiple zeta sums," *Math. Comp.*, 67, 223, 1163-1172

Buhler, J., Crandall, R., Ernvall, R., Matsankayla, T. and Shokrollahi, 1996, "Irregular primes and cyclotomic invariants to eight million," *J. Symbolic Computation* 11

Crandall, R. E. and Buhler, J. P. 1995, "On the evaluation of Euler sums," *Experimental Mathematics*, 3, 4, 275-285

Crandall, R., Doenias, J., Norrie, C. and Young, J.1995, "The twenty-second Fermat Number is composite," *Math. Comp.*, 64, 210, 863-868

Crandall, R. E. and Fagin, B. 1994, "Discrete weighted transforms and large-integer arithmetic," *Math. Comp.*, 62, 205, 305-324 (January)

Buhler, J., Crandall, R., Ernvall, R. and Metsankyla, T. 1993, "Irregular primes to four million," *Math. Comp.*, 61, 201, 151-153

Buhler, J.P., Crandall, R.E. and Sompolski, R.W. 1992, "Irregular primes to one million," *Math. Comp.*, 59, 200, 717-722 (October)

Buhler, J.P., Crandall, R.E. and Penk, M.A. 1982, "Primes of the form n!±1 and 2*3*...*p±1", *Math. Comp.* 38, 158, (April)

Crandall, R.E. and Penk, M.A. 1979, "A search for large twin prime pairs," *Math. Comp.*, 33, [145], (January)

Crandall, R.E. 1978, "On the 3x+1 problem," *Math. Comp.*, 32, [144], (October)

E. Cahill, R. Crandall, L. Rude, A. Sullivan, "Space-time influenza model with demographic, mobility, and vaccine parameters," *Proc. 5th Ann. Hawaii Intl. Conf. on Math., Stat., and related fields*, t.b.p. 2006

www.reed.edu/epi/papers/USAfluFINAL.pdf

Crandall, R., McClellan, M., Arch, S., Doenias, J. and Piper, R. 1987, "Inverse diffusion methods for data peak separation," *Analytical Biochemistry* 167, 15-22

Russell, P. J., Crandall, R.E. and Feinbaum, R. 1984, "GELYSIS-Pascal-implemented analysis of one-dimensional electrophoresis gels," *Nucleic Acids Research*, 12, 1, 493-498

Stearns, S.C. and Crandall, R.E. 1984, "Plasticity for age and size at sexual maturity: a life-history response to unavoidable stress," In *Fish Reproduction* (eds. G. Potts and R.J. Wootton), Academic Press, pp. 13-33

Crandall, R.E. and Stearns, S.C. 1982, "Variational models of life histories," *Theoretical Population Biology*, Vol. 21, No. 5, pp. 11-23

Stearns, S.C. and Crandall, R.E. 1981, "Quantitative predictions of delayed maturity," *Evolution* 35, pp. 455-463

Stearns, S.C. and Crandall, R.E. 1981b, "Bet-hedging and persistence as adaptations of colonizers," In G.G.E. Scudder and J.L. Reveal (eds.), *Evolution today*. Hunt Institute for Botanical Documentation, Carnegie-Mellon University, Pittsburgh. pp. 371-383.

Crandall, R. E. 1997, "The challenge of large numbers," *Scientific American* (February)

Crandall, R. E. 1991, "'Idle' computers hunt for big primes," (description of my Supercomputer work) *New Scientist*, (2 Mar)

Crandall, R. E. 1991, "Symbolic processors help physics," *Computers in Physics* (Oct)

Crandall, R. E. 1990, "The NeXT computer as physics machine," *Computers in Physics*, 132-141 (Mar/Apr)

Crandall, R. E. 1988, "Notes on simulation and reality," editorial, *Computers in Physics*, (May/June)

Crandall, R. E. and Gillespie, S. G. 1987, "Welcome to the Rascal Billiard Parlour," *MacA.P.P.L.E.* (March)

Gollub, J. P. and Abraham N. B. 1986, "Physics in the colleges," (survey of modern teaching styles), *Physics Today* 28-34 (June)

McPhee, N. and Crandall, R.E. 1984, "Pascal-86 color graphics package developed at Reed College," *Intel Innovator Publication,* Vol. 5, No. 2, (June/July)

Walker, J. 1983, "Simple and vivid demonstrations of advanced concepts in physics," (survey of my experimental work) *Scientific American*, (Jan)

Crandall, R.E. 1976, "Electrical load shedding feasible if survey documents real savings," *Real Estate Forum*, New York, (July)

Crandall, R.E. and Bloom, O.A. 1976, "Existing technology reduces energy consumption by 25%," *Institutional Management*, Vol. 4, No. 5, (May)

Crandall, R. E., Klivington, J., and Kramer, D. 2004, "Gigaelement FFTs on Apple G5 clusters," (27 Aug)

Crandall, R. E. and Papadopoulos, J. 2003, "On the implementation of AKS-class primality tests," (18 Mar)

Crandall, R. E. and Papadopoulos, J. 2002, "Octuple-precision floating point on Apple G4," (8 May)

Crandall, R. E. 2000, "PowerPC G4 for Engineering, Science, and Education"

Crandall, R. E. 2000, "Fast matrix algebra on Apple G4," Advanced Computation Group, Apple Computer (29 Feb)

Crandall, R. E. and Klivington, J. 2000, "Supercomputer-style FFT library for Apple G4," Advanced Computation Group, Apple Computer (6 Jan)

Crandall, R. E. and Klivington, J. 1999, "Vector implementation of multiprecision arithmetic," Advanced Computation Group, Apple Computer (25 October)

Crandall, R. E. and Klivington, J. 1999, "Vector implementation of color-image wavelet transform," Advanced Computation Group, Apple Computer (25 October)

Crandall, R. E. 2005, U.S. Patent #6912323, "Method and apparatus for fast convolution using separated spline kernel."

Crandall, R. E. 2003, U.S. Patent #6701028, "Method and apparatus for fast convolution using spline kernel."

Crandall, R. E. and Garst B. 2001, U. S. Patent #6307935, "Method and apparatus for Fast Elliptic Encryption with Direct Embedding."

Crandall, R. E. 2000, U. S. Patent #6587563, "Cryptographic system using chaotic dynamics."

Crandall, R. E. 2000, U. S. Patent #6154542, "Method and apparatus for simultaneously encrypting and compressing data."

Crandall R. E. 1999, U.S. Patent #6433707, "Universal lossless compressor for digitized analog data."

Crandall, R. E. 1996 U. S. Patent #5581616, "Method and apparatus for Digital Signature Authentication."

Crandall, R. E., U.S. Patents #5159632 (1992), #5271061 (1993), #5463690 (1994), "Method and apparatus for public key exchange in a cryptographic system."

Crandall, R. E.; Apsell, S.; Galvin, A. 1978; U.S. Patent #4321592 "Multiple sensor intrusion detection system."

Crandall, R. E., and Morgan, D. 1974; U.S. Patent #4048620 "Central station to addressed point communication system."

Crandall, R. E. 1973; U.S. Patent #3919655 "High power operational amplifier."

2005 *Portland Business Journal*, "Reed professor, Qmedtrix put together idead," by Robin J. Moody, 23 December

2005 *The Mercury News*, "A case for giving children flu shots: Studies indicate sweeping benefits," by Esther Landhuis, 20 January [mercurynews.com] (registration required)

2004 *The Oregonian*, "Mathematical Supermodels Define Epidemic Predictions," by A. Dworkin, 28 April

"Math Lab: Computer experiments are transforming mathematics," by Erica Klarreich, *Scientific American*, 2004

"A Digital Slice of Pi: The new way to do pure math: experimentally," by W. Wayt Gibbs, *Scientific American*, 2003

Teitelbaum J 2002, "Review of *Prime numbers: A computational perspective* (by Crandall R and Pomerance C)," *Bulletin of the American Mathematical Society*, Vol. 39, No. 3, 449-454 (April)

"Are the Digits of Pi Random? A Berkeley Lab Researcher May Hold the Key" by Paul Preuss [pnl.gov]

"Pi à la Mode: Mathematicians tackle the seeming randomness of pi's digits" by Ivars Peterson [sciencenews.org]

"MATHEMATICS: Randomly Distributed Slices of p," by Seife, *Science* 2001 293: 793 [sciencemag.org] (registration required)

"Pi Keeps 'Em Guessing," *ScienceNOW* 2001: 1 [sciencemag.org] (registration required)

2000 *Science News*, "Great Computations," by I. Peterson, 4 March.

1999 Seybold Publisher's Keynote (with S. Jobs), on educational supercomputing

1998 Keynote Speech, "Breaking Numerical Records with Mathematica," Worldwide Mathematica Conference, Chicago Ill. June

1998 Lecture, "Advances in Cryptographic Algorithms: New Discoveries," Proc. RSA Conf., San Francisco, CA, Jan.

1991 Computerworld Smithsonian Award, Science Category, "Community Supercomputer"

1989 Senior Research Fellowship, San Diego Supercomputer Center

1983 AAPT Apparatus first-place award, for electronic gravity balance

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