LucasLehmer Primality Tester Presentation 1: Proposal

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Lucas-Lehmer Primality TesterPresentation 1
Proposal

• Team
• Nathan Stohs
• Joe Hurley
• Brian Johnson
• Marques Johnson

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Applications, History

• Lucas-Lehmer is a test used to search for
  Mersenne Primes.
• Mersenne Primes are primes of the form 2p 1
• Given p, will conclusively determine primality
  after p-2 iterations of the algorithm.
• Computationally heavy, but numbers tested
  independently, so easily distributable.
• Difficultly lies in choosing an implementation
• www.mersenne.org

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Applications, contd.

• A hardware implementation of this algorithm is
  not going to save any lives. Why important then?
• Mersenne primes (found with this test) are the
  largest prime numbers we know of today.
• A pool of over 70,000 computers currently run an
  implementation of this algorithm, with aggregate
  performance peaking at 14 Teraflops.
• This is not intended to be a commercial product.
• www.mersenne.org/primenet/

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Algorithm

• Somewhat basic.
• Mp is Prime iff
• Simple iterative structure, with p iterations
• Includes modulo, squaring, arithmetic
• Need for fast squaring

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Design

• Are we going to be able to beat a 4 GHz Pentium 4
  implementing this algorithm in hand optimized
  assembly using FFTs for squaring?
• No.
• However, it would use much less power
• Design is limited by the maximum value of p which
  we want to test, due to squaring.
• Design scales quite nicely with max p

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Flowchart
Squaring operation will dominate the design in
layout area Approx 10k-15k transistors
Due to math constraints, will not require full
blown divison Approx 4k-5k transistors
Check for 0 residue on last iteration
Arithmetic, registers, other controls Approx 3k
transistors
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Problems

• Will never be able to test untested numbers, at
  best an experiment for future work.
• A lot will depend on how we implement the
  squaring, leading too..
• May be too easy! Backup plan is to use FancyMath
  to aid performance and make the project more
  interesting.
• Other ideas considered
• Implementation of Blowfish Cipher