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    Re: Where to find theory?

    These is some discussion about models for SOB estimates in the thread on A Resource Allocation Model and the thread on A New Estimate for finding Primes above 3M. Be aware that late in the second...
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    But to really be sure, we would have to double...

    But to really be sure, we would have to double check every exponent below the new prime, just like GIMPS must double check each exponent to be sure they haven't missed any primes. The smallest...
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    Right now, with the sixth prime coming right...

    Right now, with the sixth prime coming right where this model predicted, the results would not be a lot different. Back when I was updating these calculations on a regular basis, people were unhappy...
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    As the example shows, the optimal point is a bit...

    As the example shows, the optimal point is a bit above the cube root of the error rate.
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    Actually, the double check does not need to be...

    Actually, the double check does not need to be done. Seventeen or Bust is not trying to find the smallest prime, we are trying to find any prime. The last time I checked, we hadn't found any...
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    You'll find answers to these questions in the...

    You'll find answers to these questions in the thread on a Resource Allocation Model. The best estimates of error rates at that time were extremely low - we were experiencing much lower error rates...
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    k=55459 n=8325694

    k=55459 n=8325694
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    Sixth Prime Came on Schedule

    From a closed thread:


    The Sixth came in the middle of its doorway.
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    A much smaller sample, but I've noticed that...

    A much smaller sample, but I've noticed that ElevenSmooth, another mathematical distributed computing project, is heavily weighted with Europeans, also with a wide spread of countries. In pondering...
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    The Proth-Weight estimates can be used to find...

    The Proth-Weight estimates can be used to find the probability some exponent in a range is prime. This calculation is theoretically the number of candidates left after you remove those divisible by...
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    We are presently testing in the vicinity of...

    We are presently testing in the vicinity of n=4.2*10^6. Thus

    x=k*2^(4.2*10^6)+1

    ln(x) = ln(k)+4.2*10^6*ln(2)

    If we had done no trial factoring nor P-1 factoring, the probability an...
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    Re: chance of a prime?

    The probability that any exponent is a prime is the Proth Weight for the k value divided by ln(x). This is the prime number theorem weight adjusted for the unusual divisibility properties of Proth...
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    The record for ECM just increased to 57 digits...

    The record for ECM just increased to 57 digits
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    The World Record for P-1 Factoring...

    The World Record for P-1 Factoring is 47 digits. For ECM factoring it is 54 digits. Something in this range should be high enough.
  15. Thread: P-1 factorer

    by wblipp
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    On further reflection, the proposal of 1.25 may...

    On further reflection, the proposal of 1.25 may be too low. While it's true that "a rule of 4" means that when we find a prime we will have double checked 25% of the results, there is the question...
  16. Thread: P-1 factorer

    by wblipp
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    28,688

    Suppose our error rate, presently zero, becomes...

    Suppose our error rate, presently zero, becomes 1%. At this point the earliest time it makes sense to do a double check would be when the new exponents are 3.8 times the double check exponents. At...
  17. Thread: P-1 factorer

    by wblipp
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    28,688

    There is an easy question and a hard question. ...

    There is an easy question and a hard question. The easy question is which numbers to test - I think it's clear that we want to stay a short ways ahead of the prp testing - far enough ahead that we...
  18. Thread: P-1 factorer

    by wblipp
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    28,688

    First thing I noticed is the specifying B1 and B2...

    First thing I noticed is the specifying B1 and B2 using "e" notation doesn't work, although it works fine in GMP-ECM. For example B1 as 5e4 is read as B1=5.
  19. Thread: P-1 factorer

    by wblipp
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    28,688

    It's an interesting design question whether P-1...

    It's an interesting design question whether P-1 (and possibly P+1) factoring should be done separately, like sieving, or should be integrated into the SoB client to be performed automatically as part...
  20. Thread: P-1 factorer

    by wblipp
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    28,688

    I think GMP-ECM has expression expansion already....

    I think GMP-ECM has expression expansion already. At least the 5.1-beta that I got from the Yahoo PrimeNumbers Group would accept expressions like 4847*2^300087+1.
  21. Thread: P-1 factorer

    by wblipp
    Replies
    385
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    28,688

    The crashing on large numbers happens because the...

    The crashing on large numbers happens because the standard build uses the local memory stack, and this overflows when storing large numbers. According to Paul Zimmermann, the author of GMP-ECM, to...
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    I see that for exponents in the range of 15...

    I see that for exponents in the range of 15 million, GIMPS does trial factoring to 2^65, whiich is almost 4*10^19. They must be harder to shock.



    0.1% of resources devoted to sieving is...
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    This part isn't right - it's an artifact of using...

    This part isn't right - it's an artifact of using the 50 percentile milestone as a substitute for finding the next prime. We have what the reliability folks call increasing residual lifetime - that...
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    The model knows that only sieved values above the...

    The model knows that only sieved values above the current test point increase the progress of testing. First the sieving differential equation determines the sieving level at time t. After that has...
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    First Model Results Reveal Model Flaw

    The major results are that within wide bounds the sieving level doesn’t matter much and that our model has failed to capture an important aspect of the system. More on this failure and what I'm...
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