Largest number checked?

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Ok, it's nice that we have a list of the numbers with the most steps to complete the collatz sequence, but shouldn't we also make public the highest integer that has been checked? | |

ID: 6270 · Rating: 0 · rate:
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Ok, it's nice that we have a list of the numbers with the most steps to complete the collatz sequence, but shouldn't we also make public the highest integer that has been checked? The project started at 2,361,183,346,958,000,000,001. At the time I started writing this, 2,362,732,763,790,994,811,240 was the start of the next new WU. Therefore, Collatz volunteers have computed or are in the process of computing the steps for 1,549,416,832,994,811,239 numbers (1.5 quintillion numbers) since the project began. In the last couple minutes, the next WU number has increased to 2,362,733,109,518,682,270,056. In other words, the actual number is pretty much useless. I am working on something that will give more daily feedback though. Stay tuned... | |

ID: 6273 · Rating: 0 · rate:
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is there any reason about 2,361,183,346,958,000,000,001 as the starting number? | |

ID: 6345 · Rating: 0 · rate:
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still no one has any idea? | |

ID: 6525 · Rating: 0 · rate:
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Probably some home-testing from Slicker & Co, to cover the gap between the 3x+1@H and Collatz. | |

ID: 6589 · Rating: 0 · rate:
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Who knows, maybe Slicker is planning something? ;) | |

ID: 6591 · Rating: 0 · rate:
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is there any reason about 2,361,183,346,958,000,000,001 as the starting number? The overlap was extremely cautious. While 3x+1 reported the highest steps for their finishing number, we don't know whether ALL workunits were returned from all of the previous numbers or not. Therefore some overlap was required. The overlap was also helpful in checking that the new apps matched the original 3x+1 findings. Was the overlap too large. Yes. I hadn't intended an overlap of that much, but by the time I realized it, we were about at the end of their findings anyway. That worked out OK because I wasn't 100% sure of the results with all the validate problems we had with the 1.xx apps. [quote]... but shouldn't we also make public the highest integer that has been checked?[]/quote] If every person completed every WU they returned successfully, then yes. The problem is that there are "holes" all over that are waiting for WUs to be resent. Some time out. Some are aborted. Some are from detaching. Regardless of the reason, just because someone got a new highest number in their WU, it doesn't mean that all the numbers lower than it have been checked. For example, today we had a WU returned that found the highest steps for: 2,363,058,707,999,594,908,095 But we also had a WU today which returned the steps for: 2,362,904,828,965,727,392,679 Since there are "only" 200 billion numbers per WU, that equates to 769,000 workunits between them and yet they were returned on the same day. Could the same have happened in the original 3x+1? I don't know as I don't have all the stats, just the final list of numbers with lots of steps. We will probably be going back and picking up some numbers that are in a range much lower than what we are currently working on now. It seems that there was a gap between where others left off and where the 3x+1 started. I don't know if that was random or agreed upon. I'd also like to come up with a way to guarantee that the results are valid w/o requiring a wingman. When? Not this month. I'm up to my eyeballs in work with my second job as I (stupidly - hindsight being 20/20) decided an upgrade for the report software would fix some problems (which it did) but only to discover it now formats the dates differently and the memory deallocation has changed. So, I now have 200 reports to upgrade and test which doesn't leave much time for Collatz other than just keeping it running. Hopefully, I'll have more time in a couple weeks to start working on this (and the Collatz server upgrade). | |

ID: 6593 · Rating: 0 · rate:
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I've been thinking about this search. Are we looking through numbers one by one, or do you do some kind of sieving beforehand (most obvious that come to mind are powers of 2)? If not, would it make sense to store numbers found during a search that are bigger than the starting number, so that they can be eliminated from later searches? | |

ID: 6842 · Rating: 0 · rate:
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Are we looking through numbers one by one, Yes. or do you do some kind of sieving beforehand (most obvious that come to mind are powers of 2)? No. As I said some time before, there are virtually no powers of 2 in the WUs (no WU calculated up to date by this project contained one). There exist some sieving algorithms, but they are not very effective for searching delay time records (longest path to 1). But they could be put to some use for reducing the numbers of candidates one needs to check if one is only interested in disproving the conjecture or to search for the largest excursion to large values. And one needs to be extremely effective with such a sieve, as simply determining the numbers of steps down to one is really fast with the streamlined algorithm used here (a HD5870 can do it for approximately 600 million numbers per second!). So the checks for excluding some numbers from the search would effectively slow down the calculation in most cases. If not, would it make sense to store numbers found during a search that are bigger than the starting number, so that they can be eliminated from later searches? I don't hink so. As a single WU checks more than two hundred billion numbers, no database on the planet will be able to handle the amount of data that would be necessary, let alone that the data transfers to all the hosts would be prohibitive anyway. | |

ID: 6845 · Rating: 0 · rate:
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To jump ahead to arbitrarily high numbers :) #!/usr/bin/env python
# DonMorrison at gmail
import sys, gmpy
def collatz(z):
cnt = gmpy.mpz(0)
while z != 1:
cnt += 1
#print '%d' % z
if z % 2:#odd
z = 3 * z + 1
else:#even
z = z / 2
print 'Total iterations before reaching 1: %d' % cnt
collatz(gmpy.mpz(sys.argv[1])) | |

ID: 8209 · Rating: 0 · rate:
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This too counts completely back to 1. | |

ID: 8331 · Rating: 0 · rate:
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Ethian: Yes, there are various tradeoffs you can make depending on your goals. The goal of my post was to let the curious check an arbitrary number easily. Python is an easy and interactive means to do so -- that script runs on Ubuntu if you just install the python-gmpy package, or on MacOSX with the py-gmpy package (macports). Of course, it's not designed to be particularly fast. | |

ID: 8340 · Rating: 0 · rate:
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The drawback is that you loose the records, so you don't know how long exactly it took to get to 1. I do not think that Slicker keeps the records about each and every number checked. In fact, each wu checks millions of numbers but reports back about the steps of the longest one... | |

ID: 8414 · Rating: 0 · rate:
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I know that he won't even try to keep a database with how long the numbers take to get to 0, but you can't even know which one takes longest to 0, only which one takes longest to get below the original value. Depending on that number, it may or may not take ages to get to the 4-2-1-cycle. | |

ID: 8430 · Rating: 0 · rate:
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Ethian: Thanks for the enthusiasm and the compliment! One point of difference: you cannot prove the conjecture is true by trying all positive numbers, since they are infinite. | |

ID: 8436 · Rating: 0 · rate:
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ty ;) | |

ID: 8541 · Rating: 0 · rate:
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Here's a short Sage (python) program that searches for counterexamples, and displays a graph. It assumes your low input parameter will be 3 mod 4 since a counter-example is supposed to be 3 mod 4 (citation on wikipedia or mathworld.) I could be wrong, I skimmed it. :-) It could be more efficient...but it makes more pretty graphs. def collatz(z):
i = 0
zin = z
while z > 1:
i = i + 1
if z % 2:
z = 3 * z + 1
else:
z = z / 2
return (zin, i)
def mys(lo, hi):
lst = []
while lo < hi:
lst.append(collatz(lo))
lo += 4
return list_plot(lst)
#mys(3+2^58, 3+2^59) | |

ID: 8546 · Rating: 0 · rate:
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Ethian: it's log-linear, or at least appears to be for as far as can be quickly computed. It's easy to modify that small program I posted to change the x-axis to log(input). I misspoke though, it, of course, does not detect non-trivial cycles (counter-examples)...so it's just for fun.... :) | |

ID: 8577 · Rating: 0 · rate:
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Slicker: What's the highest work unit received to date, can ya share? Taking the numbers from your posts above, it sounds like we're working in the [2^71,...) range. | |

ID: 8660 · Rating: 0 · rate:
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Slicker: What's the highest work unit received to date, can ya share? Taking the numbers from your posts above, it sounds like we're working in the [2^71,...) range. The new workunits will now contain the starting number and the length in the name. For example, if the WU is named collatz_2367871917423103551848_824633720832 that means it starts at 2,367,871,917,423,103,551,848 and will be checking 824,633,720,832 numbers. The last _0, _1, _2, etc. are the number of times it has been sent. _0 and _1 are normal. You will only see _2, _3, and higher when one of the first two errors out, times out, or is aborted. | |

ID: 11191 · Rating: 0 · rate:
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