# Curt Noll's Primes

The 25th and 26th Mersenne primes were found by Laura Nickel and Landon Curt Noll at age 18. Although both Noll and Nickel were in high school at the time, they were both studying number theory under Dr. Lehmer (who developed the modern test for Mersenne primes) and Dr. Jurca (a CSUH math professor). Noll was also attending Cal State University at Hayward as a freshman. After their results were confirmed by Dr. Lehmer and an abstract was received by Math Comp, their press announcement was reported around the world (NBC nightly news, BBC, Tass, ...).Noll and Nickel began their Mersenne prime search at M_{21000}
using idle cpu time on the Cal State University Cyber 174. A primary motivation
for the search was the Noll-Nickel Mersenne island conjecture. Tuckerman,
the discoverer of M_{19937} had stopped at M_{21000}:
"barely on the beach" of a Mersenne island. In the optimistic words of
Dr. Lehmer that:

"happiness is just around the corner"Noll and Nickel discovered, on 30 Oct 1978, that Tuckerman's island contained M

_{21701}. Using an improved search program, Noll independently went on to show on 9 Feb 1979 that this same island also contained M

_{23209}.

Between the M_{21701} and M_{23209} discovery, Noll engaged
in several exchanges with David Slowinski and Harry Nelson - co-discoverers
of M_{44497}. Noll gave them extensive factoring tables, suggestions
on how to perform a fast modulus has well as his prediction that the next
Mersenne island was likely to be near the Mersenne island centered near
M_{44500}. Slowinski and Nelson missed the discovery of M_{23209}
by a few weeks.

Noll's Mersenne prime searching days largely ended when he came to the
end of the Mersenne island at M_{24500}. Even so, Noll continued
to investigate better methods for primality testing. Motivated by a conversation
with Gene Smith at a West Coast Number Theory conference, Noll helped
co-form the 'Amdahl 6' team of:

Joel Smith, John Brown, Landon Curt Noll, Bodo Parady, Gene Smith and Sergio ZarantonelloUsing by Noll's observation that:

Even though the Lucas-Lehmer test is the most efficient known definitive test for large primes, searching for Mersenne primes is not the most efficient way to discover a new largest known primethe 'Amdahl 6' team developed a general primality search method for primes of the form

*k**2^

*n*+/-1. On 6 Aug 1989 the 'Amdhal 6', using an Amdahl 1200 proved that 391581*2^216193-1. At the time of discovery, it was the largest known prime and is still the largest known non-Mersenne prime (as of March 1996).

The 'Amdahl 6' team went on to discover, 663777*2^7650+/-1, 571305*2^7701+/-1 and 1706595*2^11235+/-1; each of which was a 'largest known twin prime' at the time of discovery. The 'Amdahl 6' also contributed many large Titanic primes including what they like to call the "largest easy to remember prime": 235235*2^70000-1. :-)

Laura Nickel is now known as Ariel Glenn and is rumored to be somewhere at NYU. Brown, Noll and Zarantonello currently consume large number cpu cycles while working for Silicon Graphics (who now owns Cray Research). Noll is also the Vice Mayor of Sunnyvale. Gene Smith is doing post-doc mathematics work, Bodo Parady works for Sun Microsystems and Joel Smith works for Amdahl.

(This page was written in 1995)