Odd Perfect Numbers are Greater than 10^1500
Résumé
Brent, Cohen, and te Riele proved in 1991 that an odd perfect number N is greater than 10^300. We modify their method to obtain N > 10^1500. We also obtain that N has at least 101 not necessarily distinct prime factors and that its largest component (i.e. divisor p^a with p prime) is greater than 10^62.