The composite cofactor of 3,637- was the product of 85-digit and 127-digit prime numbers:

85-digit prime factor:
2436237179004869103642947050886873552395236007163725889114267732351631395223998169289

127-digit prime factor:
1295620637721513291344046150199019240130469543221325214558795515080650922339897532747195922323001636473409360593989593377975691

Thanks go to M. Vang for performing the postprocessing. The factors have been reported to the Cunningham project and have been recorded on Page 125.