Professor Richard Crandall Is at His "Primes"
Professor Richard E. Crandall is a renowned
scientist, author, and long-time Mathematica user who specializes in
developing algorithms for interdisciplinary use. He is an Apple
Distinguished Scientist and also serves as Director of the Center for
Advanced Computation and Telecommunications in Portland, Oregon, where he continues his
interdisciplinary research and Apple contributions.
Crandall has been a Mathematica user for more than a decade. He used
Mathematica prototyping in the late 1980s to develop the IBDWT (irrational
base discrete weighted transform) algorithm that is now in wide use in
large-prime searches. In fact, the four most recent, largest known primes
(the latest being 2^13466917 - 1) were all found with his IBDWT algorithm.
With a doctorate from MIT, Crandall has worked at length in both the commercial
and the academic realms and has received a number of national awards and
distinguished appointments. In all, he has authored over 60 papers,
several textbooks, and eight U.S. patents. Among his many papers are yet
other examples of Mathematica successes. His work on space-filling curves
grew almost exclusively out of Mathematica manipulations. His papers on
lattice sums--notably the Madelung constant--also made heavy use of
Mathematica during the research phases. His work on the quantum zeta
function necessitated powerful symbolic algebra machinations, and so
Mathematica again played a central role.
Likewise, the prototyping work for studies of large Fermat numbers were
in Mathematica, as was the Fast Elliptic Encryption (FEE) system of
ultrafast elliptic algebra applied to cryptography, invented at NeXT, Inc.
in the 1980s and now owned by Apple. In fact, along with these very early
Mathematica forays, Professor Crandall also designed some of the
evaluation schemes for special functions that now reside in Mathematica
itself. More recently, the popular Bailey-Crandall theory of chaotic
dynamics and normal numbers involved Mathematica prototyping.
As a professor, Crandall has also used Mathematica extensively in his
teaching. He likens the typical computer-course classroom of the 70s and
80s to a hospital "crowded with the wounded, both students and teachers
because it used to be tough to teach high-level programming languages. Few
students could handle the sudden paradigm shift from theoretical texts to the
actual code that was involved. "Now we have Mathematica," says Crandall,
"which is not always the ultimate programming/teaching tool, but it
certainly enjoys a very high batting average in the classroom." He adds,
"Show me a population biology student who is interested in the chaos
in the discrete logistic system for species competition, and I shall show
you a future Mathematica aficionado."
Crandall, the Mathematica aficionado, has been at it again. His
latest work was coauthored with esteemed number theorist Carl
Pomerance and is entitled Prime
Numbers: A Computational Perspective. This recent book
attempts to explain in plain English what is being done in advanced
number-theoretical algorithms of today. Crandall and Pomerance also
released a companion code set, PrimeKit, which contains
the Mathematica support code for all 112 algorithms discussed
in the book as well as an implementation of the celebrated AKS
The book has been quite well received and is now in its second printing,
which incorporates a variety of updates. "It's rare to say this of a math
book, but open Prime Numbers to a random page and it's hard to put down,"
says a review in the Bulletin of the American Mathematical Society.
Prime Numbers: A Computational Perspective and the companion PrimeKit are
both available through the Wolfram Research web store. For more information
about Professor Crandall's works and accomplishments, visit his company's website.