Оn March 24, 2017 our “3000 Collatz Tester” tested the 31st Mersenne prime M216091 for being in agreement with Collatz conjecture and supported it.

M216031 required 2906179 steps to get from 7.46*10⁶⁵⁰⁴⁹ to 1. In the process the sequence took 432181 first steps to expand by 1.09*10³⁸⁰⁵² times.

Full statistics for М216091 Collatz sequence is presented below.

TESTED COLLATZ SEQUENCE FOR M216091 HAS THE FOLLOWING STATISTICS:
NUMBER(N) = 7.460931E+65049
DIGITS in NUMBER(N) = 65050
BITS in NUMBER(N) = 216091
MAXIMUM(N) = 8.129870E+103101
DIGITS in MAXIMUM(N) = 103102
BITS in MAXIMUM(N) = 342498
STEPS to MAXIMUM(N) = 432181
BASIC EXPANSION(N) = 1.089659E+38052
DIGITS in BASIC EXPANSION(N) = 38053
BITS in BASIC EXPANSION(N) = 126407
EXPANSION(N) = 0.000000E+0
DIGITS in EXPANSION(N) = 0
BITS in EXPANSION(N) = 0
GLIDE(N) = 1350263 (46.0%)
EVEN(N) = 1865511 (64.2%)
ODD(N) = 1040668 (35.8%)
DELAY(N) = 2906179 (100.0%)
COMPLETENESS(N) = 0.557846
RESIDUE(N) = 1.184517
GAMMA(N) = 12.454769
STRENGTH(N) = -393193
LEVEL(N) = 49150

The definitions for presented parameters are given at Eric Roosendaal’s site.

The next number that we test will be the 32nd Mersenne prime M756839.