Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis
08-17-2017, 07:56 PM
Post: #45
 Werner Senior Member Posts: 695 Joined: Dec 2013
RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis
Well, that is the challenge as numbers keep growing ;-)
For x < 1e17, I can cube it exactly quite easily, as Free42 carries 34 digits, so
x^3 calculated as x.x^2 has a single roundoff error

Then,
x^3 = B + r, where
r = MOD(x^3,1e17) = MOD(x.MOD(x^2,1e17),1e17) (for x<1e17, x^2 is exact)
r are the 17 trailing digits of x^3
B = x^3 - r, a number (< 1e51) ending in 17 zeroes.

By tomorrow I will have passed 1e51 for x^3 and I'll have to find something new.

PS. Currently running with the 20 million numbers < 1e12 that, when cubed, have the trailing 12 digits in {2,3,5,7} and narrowing down the cubes to match the first 8 digits. Verification of a number focuses first on the digits 'in the middle' as we know that the 8 leading and 12 trailing digits are all 2,3,5 and 7
Verifying cubes larger than 1e50 and smaller than 1e51 will take 3.5 hours, estimated.
Pre-computing an extra order of numbers speeds up the process by a factor 2.5, but order 12 seems to be the maximum, memory-wise. REGS can hold the 20 million, but not the 80 million needed for order 13.

Cheers, Werner
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Massimo Gnerucci - 08-07-2017, 07:14 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Gerald H - 08-07-2017, 07:56 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - AlexFekken - 08-07-2017, 10:33 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - AlexFekken - 08-07-2017, 10:50 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-07-2017, 07:09 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-08-2017, 06:38 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Arno K - 08-08-2017, 01:50 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-07-2017, 07:57 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-08-2017, 12:01 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Gerald H - 08-08-2017, 03:10 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Paul Dale - 08-08-2017, 12:53 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-08-2017, 03:39 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-09-2017, 03:20 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-10-2017, 08:17 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-11-2017, 04:43 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-11-2017, 10:26 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Gerald H - 08-08-2017, 05:20 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Joe Horn - 08-09-2017, 01:02 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-09-2017, 02:27 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Joe Horn - 08-10-2017, 03:51 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Gerald H - 08-10-2017, 07:34 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Paul Dale - 08-10-2017, 07:44 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Joe Horn - 08-10-2017, 01:26 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-10-2017, 02:41 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Arno K - 08-11-2017, 04:57 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-14-2017, 10:11 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-15-2017, 04:31 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-15-2017, 12:20 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-15-2017, 08:51 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-16-2017, 04:26 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Gerald H - 08-16-2017, 04:51 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-17-2017, 12:50 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-17-2017, 03:11 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - pier4r - 08-17-2017, 05:06 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-17-2017 07:56 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - pier4r - 08-17-2017, 08:50 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-18-2017, 03:47 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Joe Horn - 08-18-2017, 11:51 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-21-2017, 02:10 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - pier4r - 08-21-2017, 03:39 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - David Hayden - 08-21-2017, 08:39 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Claudio L. - 08-23-2017, 12:03 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-23-2017, 03:20 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Claudio L. - 08-23-2017, 09:15 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-23-2017, 09:58 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Claudio L. - 08-23-2017, 11:53 PM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - DavidM - 08-24-2017, 12:54 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Werner - 08-24-2017, 09:08 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - pier4r - 08-24-2017, 11:47 AM RE: Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis - Paul Dale - 08-24-2017, 08:37 AM

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