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.