Forum: Miscellaneous Math
2018-12-09, 05:17
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Replies: 8
Views: 853
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...
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Forum: Miscellaneous Math
2018-12-09, 00:52
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Replies: 8
Views: 853
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
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Forum: Miscellaneous Math
2018-12-09, 00:15
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Replies: 8
Views: 853
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...
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Forum: Miscellaneous Math
2018-12-08, 22:45
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Replies: 8
Views: 853
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Forum: Puzzles
2018-12-08, 20:11
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Replies: 31
Views: 2,107
Goldbug's Algorithm!
See the latest puzzle involving Goldbug's algorithm here:
https://www.mersenneforum.org/showthread.php?p=502097#post502097
Have fun!
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Forum: Miscellaneous Math
2018-12-08, 19:55
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Replies: 8
Views: 853
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...
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Forum: Puzzles
2018-12-07, 18:40
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Replies: 31
Views: 2,107
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?
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Forum: Puzzles
2018-12-06, 18:59
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Replies: 31
Views: 2,107
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!
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Forum: Puzzles
2018-12-06, 18:52
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Replies: 31
Views: 2,107
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Forum: Puzzles
2018-12-06, 01:50
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Replies: 31
Views: 2,107
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Forum: Puzzles
2018-12-05, 15:03
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Replies: 31
Views: 2,107
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...
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Forum: Puzzles
2018-12-05, 10:04
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Replies: 31
Views: 2,107
This is so amazing uau!?! So interesting...
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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...
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Forum: Puzzles
2018-12-05, 03:37
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Replies: 31
Views: 2,107
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...
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Forum: Puzzles
2018-12-05, 01:52
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Replies: 31
Views: 2,107
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...
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Forum: Puzzles
2018-12-05, 00:01
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Replies: 31
Views: 2,107
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Forum: Puzzles
2018-12-04, 15:25
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Replies: 31
Views: 2,107
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Forum: Puzzles
2018-12-04, 13:39
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Replies: 31
Views: 2,107
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...
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Forum: Puzzles
2018-12-04, 12:11
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Replies: 31
Views: 2,107
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...
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Forum: Puzzles
2018-12-04, 00:08
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Replies: 31
Views: 2,107
#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...
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Forum: Puzzles
2018-12-03, 19:00
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Replies: 31
Views: 2,107
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Forum: Puzzles
2018-12-03, 18:32
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Replies: 31
Views: 2,107
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....
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Forum: Puzzles
2018-12-03, 02:37
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Replies: 31
Views: 2,107
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...
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