Factors for (141^141 + 142^142) and (148^148 + 149^149) Discovered by Mr. Stolyarov and ECM Distributed Computing Project

# Factors for (141^141 + 142^142) and (148^148 + 149^149) Discovered by Mr. Stolyarov and ECM Distributed Computing Project

G. Stolyarov II
August 28, 2012
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Since the discovery in April 2012 of a factor for (118^67 + 67^118), I have continued to donate extensive computing resources to the ECM distributed computing project (organized via Yoyo@home). Today I am pleased to announce that two more large factors of even larger numbers have been discovered as a result of this endeavor. I am credited with the discoveries here. The following is now known:

● The number (141^141 + 142^142) (see long form here) has a 33-digit factor: 168,853,190,844,095,597,109,245,277,698,729.

● The number (148^148 + 149^149) (see long form here) has a 28-digit factor: 9,055,497,748,306,357,299,810,062,467.

To date, my computer has examined 2729 project workunits (each involving an attempt to factor a large number). I have thus far accumulated 528,533.42 BOINC credits for the ECM project.

The magnitudes involved are astounding, considering that the factors discovered are several hundred orders of magnitude less than the original numbers. As an example, (148^148 + 149^149) is equal to approximately 6.39 * 10^323. And yet our advancing technology is enabling us already to explore these immense quantities and derive meaningful conclusions regarding them.

## 2 thoughts on “Factors for (141^141 + 142^142) and (148^148 + 149^149) Discovered by Mr. Stolyarov and ECM Distributed Computing Project”

1. Jim Wright says:

Mr. Stolyarov, Now that you’ve achieved this tremendous numbers, what do you plant to do with them? Jim

2. There are some applications in elliptic-curve cryptography. See these articles for more details (this one is more basic, while the Wikipedia entry delves into the mathematics).

More generally, the purpose of these projects is to mobilize “grassroots” participation in research endeavors and to make good use of otherwise idle computer time. The mathematics projects (such as ECM or the Great Internet Mersenne Prime Search) are ways of motivating additional interest in distributed computing, as well as getting more people to participate while attaining specific achievements to show for it. As we get more participants (and as personal technology advances in power), the projects can become increasingly ambitious. Other projects I participate in predict protein-folding configurations or help to efficiently run lab tests involved in researching cures for cancer, malaria, and other illnesses.