DataTerminology.comNEW
A multiplicative linear congruential generator using xn+1 = (a·xn) mod m with carefully chosen prime moduli and multipliers.
DESCRIPTION
The Lehmer generator is a multiplicative LCG (increment zero) that achieves good spectral properties with appropriate parameters. Popularized variants include the Park–Miller “minimal standard,” which specifies prime modulus and multiplier for acceptable baseline quality. Despite improvements over naive LCGs, Lehmer generators are not cryptographically secure and can exhibit correlations. They remain useful as simple, fast PRNGs and baselines in performance comparisons.
ALTERNATIVE DEFINITIONS
Wikipedia
The Lehmer random number generator is a multiplicative linear congruential generator (LCG).
Classifies it as the multiplicative LCG family succinctly.
Park & Miller (1988)
We propose a ‘minimal standard’ Lehmer generator with carefully chosen modulus and multiplier that produces acceptable results for many applications.
Introduces the widely referenced minimal standard parameterization.
RELATED TERMS
Linear Congruential Generator Minimal Standard Park–Miller LCG Modulus Multiplier Seed Pseudorandom Number Generator Randomness Testing
COMPETING TERMS
Permuted Congruential Generator Mersenne Twister
RELATIONS
- Broader: Random Number Generator
KNOWLEDGE AREAS
Mathematics Data Science Software Engineering Testing & Validation
TARGET AUDIENCE
Data Scientist Software Developer Data Engineer
EXTERNAL SOURCES
- Wikipedia - Lehmer random number generator
- GNU Scientific Library - Lehmer/‘minstd’ PRNG in GSL
- ACM (Park–Miller) - Minimal standard parameters
TOP QUESTIONS
What distinguishes the Lehmer Random Number Generator from general LCGs?
It is the multiplicative case (no increment) with parameters selected for strong spectral properties.
Category: Concept
What are the Park–Miller ‘minimal standard’ parameters?
A classic prime modulus and specific multiplier that deliver acceptable baseline quality; see the original 1988 paper.
Category: Example
Is the Lehmer generator cryptographically secure?
No. It’s predictable and vulnerable to state recovery; use CSPRNGs for security.
Category: Risk
Where is the Lehmer generator still useful?
As a simple, fast baseline in benchmarking, teaching, and non-critical simulations.
Category: Relevancy
How does modulus choice affect period?
With proper multiplier and prime modulus, full period m−1 is achievable for nonzero seeds.
Category: Requirements
Can Lehmer generators be parallelized?
Use jump-ahead via exponentiation modulo m or assign distinct seeds; verify independence.
Category: BestPractice
What is a common pitfall when implementing Lehmer PRNGs?
Overflow in intermediate multiplication; use 128-bit arithmetic or modular multiplication techniques.
Category: Mistakes
How does Lehmer compare to PCG?
PCG adds permutation and better statistical properties while preserving speed and simplicity.
Category: Alternatives
What tests should vet a Lehmer implementation?
Start with TestU01 SmallCrush/Crush, then application-specific validation for correlations.
Category: Testing