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# Mersenne.ca

**Mersenne.ca** is a collection of web-based utilities of interest to GIMPS contributors, especially those working outside the standard PrimeNet-assigned work types.

## Contents

## History

The site's original name, **mersenne-aries.sili.net**, derives from a former project on the MersenneForum, *Marin's Mersenne-aries*, which did P-1 factoring on exponents that already had one (or more) Lucas-Lehmer test done, and not yet a matching double-check, and either no P-1 factoring done, or done with very low bounds such that the probability of finding a factor is very low. By doing P-1 tests on these numbers, it was hoped to save unnecessary double-checks. At that time (before PrimeNet v5 was created), P-1 tests were given almost zero credit (actually 0.001 P90 years), and combined with the facts that P-1 tests (can) take a large amount of RAM, and have no possibility of finding a Mersenne prime, many GIMPS users purposely skipped the P-1 stage to spend more time doing L-L first-time tests.

**mersenne-aries.sili.net** was created as a place to collect results and compare statistics for contributors working outside the normal PrimeNet work types and ranges, including *Marin's Mersenne-aries* and Lone Mersenne Hunters, since at the time PrimeNet did not offer anything comparable. After PrimeNet v5 was released, the stats portion of the site was retained, but the focus is now on calculators and utilites not available on PrimeNet.

The site was moved to its own domain, mersenne.ca, in September 2012.

## Exponent & Factor Details

Each exponent has a detailed page listing known tests (trial factoring, P-1, ECM and L-L) and all known factors. More detailed analysis is provided for known factors: k values are calculated, as well as the effort required to find the factor by TF and/or P-1. Any exponents with multiple known factors will also include a similar analysis for all possible composite factors. Bounds for know P-1 tests are graphed, with known factors overlaid to show how close any known P-1 test(s) were to finding the factor(s). A similar graph shows known factors in relation to trial-factoring effort.

These reports can be easily accessed with the abbreviated URL *mersenne.ca/<numbers>* where if the value is less than 2^32 it is assumed to be the exponent, otherwise it is assumed to be the factor.

Sample report: http://www.mersenne.ca/M2549119

As of October 2011, the data should include approximately 100% of known factors, 100% of double-checked L-L residues, 80% of unverified L-L residues, 10% of P-1 tests, 1% of TF. Upcoming updates to PrimeNet reports should allow for more complete data on L-L, P-1 and TF.

## Stats section

Any user can upload the contents of results.txt and the contents will be parsed and added to the stats. Work is automatically credited under GIMPS username and computer name (as recorded in the *results.txt* data). Work without any contributor information is also accepted. Since January 2011, results from mfaktc/mfakto/Factor5 are also accepted (results optionally credited for stats if user and computer name are entered). Top-10 lists are generated for both contributors (most work performed) and factors (largest/smallest) for each of P-1 factoring, trial factoring, ECM factoring and L-L testing. Graphs are generated for distribution of attempts and successes over time, and distribution of found factor sizes. Stats pages are also available for individual contributors, and for each of their computers.

## CPU Benchmarks & Throughput Calculator

The benchmarks section displays Prime95 benchmarks in a format similar to the equivalent PrimeNet v5 page, but with a little more detail in FFT sizes and trial bit depths. More data is stored than is displayed (FFT sizes from 4K to 32768K are stored, only 512K to 4096K are displayed). Users may contribute benchmark data to the site admin (direct uploading of benchmark data is not allowed). The benchmark data is also presented in a different way on the throughput calculator. The relative efficiency of any given CPU is shown at different FFT sizes, trial-factoring bit depths, and with 32-bit and 64-bit versions of the client. This helps the user pick the most efficient type of work for their particular CPU. Multiple CPUs (up to 4) can be compared directly to show relative efficiency comparison on all work types. If more than one benchmark is available for a displayed CPU, the results are scaled to a common clock speed and averaged. Estimated throughput (in GHz-days) is shown for each work type. CPU speed can be overridden to simulate overclocking.

## GPU Throughput Chart

The GPU throughput chart displays expected mfaktc/mfakto GPU trial factoring performance for most GPU models that are capable of running either program. Additional computed values such as performance-per-watt and performance-per-dollar are also calculated for each GPU model.

## P-1 Work Finder

The P-1 work finder continues the *Marin's Mersenne-arie* tradition of finding "missed" P-1 work to do, either where P-1 was not done at all, or done to very low bounds. The data is pulled directly from PrimeNet status pages (in exponent ranges of 100,000 at a time) and then the probability of finding a factor is calculated based on both trial-factoring and P-1 factoring that has been done on each exponent. Most GIMPS P-1 work is done to around 5-7% probability of finding a factor, after trial-factoring to a pre-determined bit depth. By default, exponents in the selected range with <5.00% chance of finding a factor are displayed. This takes into account exponents that have a smaller-than-usual P-1 factoring, but larger-than-usual trial factoring. Results are cached for quick access to the "worst" ranges of exponents, where large a number of exponents have been poorly factored. Most options are user-configurable to allow the user to select whatever type of P-1 work interests them. If any matching exponents are found, they are presented in a format that can be copied directly to the user's worktodo.txt file. Several graphs are displayed showing the overall distribution of P-1 probabilities.

## Graphs & Charts

Several graphs are generated nightly, including a graph representing the number of factored vs unfactored exponents and the bit size of the known factors, in granularity of 0.1-million up to 192M, and 1-million up to 4294M (M2^32-1).

## Beyond-PrimeNet Trial Factoring

**mersene.ca** also serves as a convenient factor repository for those interested in trial factoring beyond the supported range of PrimeNet (<1000M), including projects such as Operation Billion Digits. Initial pre-factoring of the 1000M to 4294M range in September 2012 eliminated approximately 1/3 of the candidates (roughly 50 million factors from approximately 150 million candidates). Initial pre-factoring looked for the smallest factor, if any, up to k=10000. Phase 2 of the factoring involves trial-factoring candidates to (at least) 2^64, using a simple anonymous reservation system.

## Other Calculators

There are a number of calculators on the site:

**PrimeNet Credit Calculator**: calculates the PrimeNet credit (in GHz-days) for any assignment type.**P-1 Probability Calculator**: calculates probability and credit for any P-1 assignment. Can also calculate the optimal bounds for a given probability or desired work-effort.**Worktodo Balancer**: evenly splits assignments across multiple workers in user-configurable sorted order*Mersenne number decimal digits calculator*: calculates the number of decimal digits in a Mersenne number, or the smallest Mersenne number with that many decimal digits.*Bit size of factor calculator*: calculates the number of decimal digits, and bit size of any decimal number (typically found factors).*GIMPS trial-factoring limits*: shows the default bit depth limit for trial factoring any exponent.*Small number prime factorization*: calculates prime factorization for small numbers (up to 45 decimal digits)