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anomalously large prime missing so far

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  • James Merickel
    Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce
    Message 1 of 7 , Jul 30, 2011
      Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
      Jim
    • Jack Brennen
      As far as how to break GP to examine the state, it might be too late if you ve been running for 5 days. If you are running GP interactively, the trick is
      Message 2 of 7 , Jul 30, 2011
        As far as how to "break" GP to examine the state, it might be too late if you've been running for 5 days.

        If you are running GP interactively, the "trick" is to execute the GP function trap() before you start your program or your script. Then hitting Ctrl-C should break you out to a prompt
        where you can examine or change variables, etc.

        On 7/30/2011 10:08 PM, James Merickel wrote:
        > Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
        > Jim
        >
        >
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      • James Merickel
        I should say for completeness that a simple ispseudoprime is being done for each adjoining. Probably batching trial divisions could speed things up quite a
        Message 3 of 7 , Jul 30, 2011
          I should say for completeness that a simple 'ispseudoprime' is being done for each adjoining. Probably batching trial divisions could speed things up quite a bit even using PARI/GP, but it would have been much harder to write. This result is somewhat surprising in comparison to somewhat similar questions, since the adjoining of only 2 digits goes on much longer, and so on. Should also say that I have no reason at all to believe a crash really occurred. Not impossible, but all other evidence I have is against it. The overtaxing may, however, be underrated by me. If the kind of calculation weights how often the processors work on one rather than another program, I suppose it's possible it would really only be a day if this program had run alone.
          Jim

          On Sun Jul 31st, 2011 1:08 AM EDT James Merickel wrote:

          >Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
          >Jim
        • James Merickel
          Here is the exact code being used and its current output: { i=1;n=0;e=10; while(i, p=prime(i);if(p e,e*=10); for(j=1,i^2,
          Message 4 of 7 , Jul 31, 2011
            Here is the exact code being used and its current output:

            {
            i=1;n=0;e=10;

            while(i,
            p=prime(i);if(p>e,e*=10);

            for(j=1,i^2,
            n*=e;n+=p;if(ispseudoprime(n),print1("("i","j") "))
            );

            i++;next()
            )
            }
            -----------------------------------------------------------------
            (1,1) (2,1) (2,2) (2,3) (2,4)

            Jim
            P.S. I answered the question more along the lines requested in a response to Mr. Hasler already, not realizing it wasn't going to the group. If anybody else really didn't understand, after the given value of 23333, nine 5s are appended and then sixteen 7s, twenty-five 11s, and so on; and the current question on the appearance of the next prime doesn't look at numbers ending after the first 1 of an 11 (and the like).

            On Sun Jul 31st, 2011 5:20 AM EDT Maximilian Hasler wrote:

            >On Sun, Jul 31, 2011 at 7:08 AM, James Merickel <merk7777777@...> wrote:
            >> Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number.
            >
            >
            >could you explain to the simple minded as me, what kind of numbers you
            >test exactly ?
            >I can't see what the n^2, nor the prime(n), refer to w.r.t. the
            >example 2,23,233,...
            >
            >
            >>.  Unless somebody knows how to break the program,
            >
            >on PARI versions not older than 2 years or so (since v.2.4.3 IIRC)
            >you can simply hit Ctrl-C, which interrupts the computation,
            >gives you a command prompt to let you examine variables and do
            >whatever nasty thing you want, and continue the computation at the
            >very point it stopped.
            >
            >
            >>the time with the CPU overtaxed, as information on where exactly in the search I am.
            >
            >so you know where you are ? can you give this information ?
            >
            >M.
          • James Merickel
            I misjudged this to be a minor rarity, as remarked to me by Jens. Had intended a rejoinder for him after a calculation, but it turns out that no prime for
            Message 5 of 7 , Aug 2, 2011
              I misjudged this to be a minor rarity, as remarked to me by Jens. Had intended a rejoinder for him after a calculation, but it turns out that no prime for placement of the 2-digit primes (through 11020 digits) is to be expected as reasonably possible at a level slightly larger than 1/4, removing essentially all interest.
              Jim

              On Sun Jul 31st, 2011 1:08 AM EDT James Merickel wrote:

              >Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
              >Jim
            • John
              I probably sent this query to James rather than the group, so I will repeat the gist of it. Is the quest for series of numbers with what essentially is the
              Message 6 of 7 , Aug 4, 2011
                I probably sent this query to James rather than the group, so I will repeat the gist of it.

                Is the quest for series of numbers with what essentially is the property of having extraordinarily low factors a Critical Theoretical Question, of is it in the nature of finding very interesting, dare I say "merely" very interesting, facts?

                Practicality is by no means the touchstone of virtue, so I am not passing this search off as a vain endeavour, of course.

                I suppose this is to do with the nature of the mysteries of numbers. It seems to many mathematical musers that in a certian sense, there is an abundance of order and pattern in numbers (relating to primality and factorability), an abundance so great that it defies fathoming.

                Is that its charm, so obvious and, yet, so eluxive?

                --- In primenumbers@yahoogroups.com, James Merickel <merk7777777@...> wrote:
                >
                > I misjudged this to be a minor rarity, as remarked to me by Jens. Had intended a rejoinder for him after a calculation, but it turns out that no prime for placement of the 2-digit primes (through 11020 digits) is to be expected as reasonably possible at a level slightly larger than 1/4, removing essentially all interest.
                > Jim
                >
                > On Sun Jul 31st, 2011 1:08 AM EDT James Merickel wrote:
                >
                > >Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
                > >Jim
                >
              • James Merickel
                Not sure anyone else is going to answer, but I would personally consider most of this to be a recreational challenge only, plus curiosity about the possibility
                Message 7 of 7 , Aug 5, 2011
                  Not sure anyone else is going to answer, but I would personally consider most of this to be a recreational challenge only, plus curiosity about the possibility of finding something pretty, at this point anyway. As a better example, I am now stuck on finding the first base-23 example of a non-trivial left-right concatenation of the first so many primes to be prime (as 23 is in base 10, this particular missing large number being, with this fact, the basis of a recent submission to Prime Curios!).
                  Jim

                  On Thu Aug 4th, 2011 12:49 PM EDT John wrote:

                  >I probably sent this query to James rather than the group, so I will repeat the gist of it.
                  >
                  >Is the quest for series of numbers with what essentially is the property of having extraordinarily low factors a Critical Theoretical Question, of is it in the nature of finding very interesting, dare I say "merely" very interesting, facts?
                  >
                  >Practicality is by no means the touchstone of virtue, so I am not passing this search off as a vain endeavour, of course.
                  >
                  >I suppose this is to do with the nature of the mysteries of numbers. It seems to many mathematical musers that in a certian sense, there is an abundance of order and pattern in numbers (relating to primality and factorability), an abundance so great that it defies fathoming.
                  >
                  >Is that its charm, so obvious and, yet, so eluxive?
                  >
                  >--- In primenumbers@yahoogroups.com, James Merickel <merk7777777@...> wrote:
                  >>
                  >> I misjudged this to be a minor rarity, as remarked to me by Jens. Had intended a rejoinder for him after a calculation, but it turns out that no prime for placement of the 2-digit primes (through 11020 digits) is to be expected as reasonably possible at a level slightly larger than 1/4, removing essentially all interest.
                  >> Jim
                  >>
                  >> On Sun Jul 31st, 2011 1:08 AM EDT James Merickel wrote:
                  >>
                  >> >Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
                  >> >Jim
                  >>
                  >
                  >
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