On September 19th, 2017 our “3007 Collatz Tester for Mersenne Primes” (the improved version of “3000 Collatz Tester”) tested the provisional 49th Mersenne prime M74207281 for being in agreement with Collatz conjecture and supported it.
M74207281 required 998401306 steps to get from 3.00*1022338617 to 1. In the process the sequence took 148414579 first steps to expand by 7.45*1013067253 times.
Full statistics for M74207281 Collatz sequence is presented below.
TESTED COLLATZ SEQUENCE FOR M74207281 HAS THE FOLLOWING STATISTICS:
NUMBER(N) = 3.003764E+22338617
DIGITS in NUMBER(N) = 22338618
BITS in NUMBER(N) = 74207281
MAXIMUM(N) = 2.236678E+35405871
DIGITS in MAXIMUM(N) = 35405872
BITS in MAXIMUM(N) = 117615759
STEPS to MAXIMUM(N) = 148414579
BASIC EXPANSION(N) = 7.446249E+13067253
DIGITS in BASIC EXPANSION(N) = 13067254
BITS in BASIC EXPANSION(N) = 43408478
EXPANSION(N) = 0.00
DIGITS in EXPANSION(N) = 0
BITS in EXPANSION(N) = 0
GLIDE(N) = 462115324 (46.3%)
EVEN(N) = 640874253 (64.2%)
ODD(N) = 357527053 (35.8%)
DELAY(N) = 998401306 (100.0%)
COMPLETENESS(N) = 0.557874
RESIDUE(N) = 1.001150E+0
GAMMA(N) = 12.459507
STRENGTH(N) = -134987494
LEVEL(N) = 16873437
The definitions for presented parameters are given at Eric Roosendaal’s site.
As far as we know, the numbers of such magnitude have never been tested so far for Collatz conjecture confirmation. Since no other Mersenne primes are known at present, we announce that the current project is over. Any additional results or findings will be published in due course.