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Forum: Miscellaneous Math 2018-12-09, 05:17
Replies: 8
Views: 812
Posted By goldbug
Cool Goldbug's Algorithm in Python!

This doesn't solve the puzzle but you should run it. I think you will find it interesting!



import sys
import math
from itertools import chain, combinations
# Python program to test...
Forum: Miscellaneous Math 2018-12-09, 00:52
Replies: 8
Views: 812
Posted By goldbug
You are no fun, I didn't want to give it away...

You are no fun, I didn't want to give it away but... try leaving out the Goldbugs, then I think it's a valid algorithm. The n=p1 thing is weird, its just a special case that happens with non-mod 4s
...
Forum: Miscellaneous Math 2018-12-09, 00:15
Replies: 8
Views: 812
Posted By goldbug
Step 1 is just complicated for existence...

Step 1 is just complicated for existence purposes. Just run the algo for all PNDs of n between n/2 and n (or (n+1)/2 and (n+1) for non mod 4's) and count the number of loops for each PND. Then take...
Forum: Miscellaneous Math 2018-12-08, 22:45
Replies: 8
Views: 812
Posted By goldbug
To clarify, by run time I just mean how many...

To clarify, by run time I just mean how many loops need to be performed. Not looking for a theoretical answer here.
Forum: Puzzles 2018-12-08, 20:11
Replies: 31
Views: 1,815
Posted By goldbug
Goldbug's Algorithm!

See the latest puzzle involving Goldbug's algorithm here:


https://www.mersenneforum.org/showthread.php?p=502097#post502097


Have fun!
Forum: Miscellaneous Math 2018-12-08, 19:55
Replies: 8
Views: 812
Posted By goldbug
A Puzzle Involving Goldbug's Algorithm

What is the expected run time for each 2n<=10,000, if the likelihood of selecting each prime non-divisor of n in Step 1 is uniform? Does this algorithm terminate for each 2n>6? If not, for which 2n...
Forum: Puzzles 2018-12-07, 18:40
Replies: 31
Views: 1,815
Posted By goldbug
Partial Proof of the Goldbach Conjecture?!?

Has anyone seen this proof? If this was correct it wouldn't prove Goldbach for all numbers, just non-Goldbugs. Looks like there is also a way to extend to some Goldbugs?


...
Forum: Puzzles 2018-12-06, 18:59
Replies: 31
Views: 1,815
Posted By goldbug
Code to Search of k-order Goldbugs

I wanted to cross post this related question from mathexchange. I have run UAU's code up to 300k with no sign of new Goldbugs... certainly not the elusive Double Goldbug!


...
Forum: Puzzles 2018-12-06, 18:52
Replies: 31
Views: 1,815
Posted By goldbug
Sorry Dr. S, what are the implications of what...

Sorry Dr. S, what are the implications of what you discovered? I am extremely interested but don't have the background to understand completely.
Forum: Puzzles 2018-12-06, 01:50
Replies: 31
Views: 1,815
Posted By goldbug
UAU, It looks like you are returning the maximal...

UAU, It looks like you are returning the maximal isolated set for each Goldbug? I noticed 128 actually has some of the subsets of the maximal sets satisfying the property as well.

I checked each...
Forum: Puzzles 2018-12-05, 15:03
Replies: 31
Views: 1,815
Posted By goldbug
Were these the only ones you found uau in 100k?...

Were these the only ones you found uau in 100k? Look at the prime factors, so interesting. Lots of big primes and powers of 2. This makes sense, it means being Goldbug is related to number of prime...
Forum: Puzzles 2018-12-05, 10:04
Replies: 31
Views: 1,815
Posted By goldbug
This is so amazing uau!?! So interesting... ...

This is so amazing uau!?! So interesting...


I was going to say, Goldbach is true for second order Goldbugs since the n-p's can't share a factor with p, n, or 2n-p. But no idea what to do with...
Forum: Puzzles 2018-12-05, 03:37
Replies: 31
Views: 1,815
Posted By goldbug
Below is code I use to check for all order...

Below is code I use to check for all order Goldbugs less than 5000. It only returns 2200. It explodes a bit running larger n, curious to see if anyone can suggest improvements. Agree with you uau...
Forum: Puzzles 2018-12-05, 01:52
Replies: 31
Views: 1,815
Posted By goldbug
Problem with the code above

Here is a weird python thing, for some reason this doesn't check primes correctly, change it to "for i in range(3,test_num):". Doesnt' seem to impact the output. Sorry, cannot seem to change it in...
Forum: Puzzles 2018-12-05, 00:01
Replies: 31
Views: 1,815
Posted By goldbug
I hear you about python, I have spent many hours...

I hear you about python, I have spent many hours chasing down indent issues. Not married to python just thought it would be accessible. One reason I posted here is I thought people would have...
Forum: Puzzles 2018-12-04, 15:25
Replies: 31
Views: 1,815
Posted By goldbug
Is Goldbach true for both non-Goldbug and Goldbug Numbers?

It seems Goldbach is true for non-Goldbugs since we are guaranteed a process for finding a Goldbach pair. Start with any prime non-divisor of n and look at 2n-p. If its prime you have a Goldbach pair...
Forum: Puzzles 2018-12-04, 13:39
Replies: 31
Views: 1,815
Posted By goldbug
Post Code to find order 2 and order 3 goldbug numbers

This code is very straightforward in order to be transparent (know what its doing) and is not the best approach clearly. It would be nice to code this up using sets/subsets in python to do k-order...
Forum: Puzzles 2018-12-04, 12:11
Replies: 31
Views: 1,815
Posted By goldbug
Order 3 #GoldbugNumbers

My code is not finding any triples, can anyone confirm this? Hard to know if the code is correct with no counterexamples to check...
Forum: Puzzles 2018-12-04, 00:08
Replies: 31
Views: 1,815
Posted By goldbug
#GoldbugNumbers

Let me know if this holds water. The numbers I am searching for satisfy the following property. Maybe there is an easier way to search besides looking each order k=2,3,4,... separately?



Given...
Forum: Puzzles 2018-12-03, 19:00
Replies: 31
Views: 1,815
Posted By goldbug
Yes I think the cases you describe will be useful...

Yes I think the cases you describe will be useful for cases of 3 or more primes since it will reduce the number of triplets that need to be checked. I still haven't wrapped my head around how to...
Forum: Puzzles 2018-12-03, 18:32
Replies: 31
Views: 1,815
Posted By goldbug
Talking Thank you so much and the challenge continues

Thanks batalov and uau for the collision suggestion and to uau for running up to 1M^2?!?


This suggestion is going to help me greatly in extending the search to triplets, quadruplets of primes....
Forum: Puzzles 2018-12-03, 02:37
Replies: 31
Views: 1,815
Posted By goldbug
Cool Can you find another number like 2200?

Here is something I am having trouble with related to Goldbach Conjecture and maybe someone has some ideas on how to improve the search? I think these numbers will be exceedingly rare if they exist...
Showing results 1 to 22 of 22

 
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