I'm puzzled. Symbolic polynomial division (with remainder) can easily be shown to be the same level of difficulty as factoring, but descriptions of the ...
... As factoring polynomials or integers? As far as I know, factoring polynomials is polynomial-time. At least factoring in Z/pZ. By the way, this underscores...
Primes in Arithmetic Progression Records at http://hjem.get2net.dk/jka/math/aprecords.htm now shows the smallest AP-k with minimal starting prime, and the AP-k...
For n up to 3,000,000, there are only 3 cases of palindromic prime pi(n) of palindromic prime n: n=3,5,11, with pi(n)=2,3,5. Can anyone find other cases? ...
... b) in http://www.primepuzzles.net/puzzles/puzz_051.htm asks for the next. It reports exhaustive searching found 3 cases with palindromic composite pi(n): ...
Define a chain of primes of length n: {p_1,p_2...,p_n} such that C(p_(k-1))=p_(k)+1 for all 2<=k<=n where C(p_(k-1)) is the p_(k-1)-th composite. Example:...
For p prime, the integer p-1 is an important quantity in certain analyses (particularly if they involve the group (Z/pZ)*), but as I recall, this integer is...
In a message dated 04/02/2005 01:54:40 GMT Standard Time, decio@... writes: So, if we're looking for an accurate numerical value of the probability that...
Two humble questions for AP gurus and theorists, but first 2 definitions. (CP-4) means a set of 4 CONSECUTIVE PRIMES NOT IN ARITHMETICAL PROGRESSION such that...
w_sindelar@...
Feb 4, 2005 3:34 pm
16025
Let q a positive integer and 1<=r<=q. Is there a theorem that tells us how many integers a, 1<=a<=q, verify a^r=1 mod(q)? I have found that: (1) if q is prime...
... A (CP-N), N>=4, is N consecutive primes with gaps alternating between two different values. ... Let a, b, c be random consecutive primes around N. They...
Sorry for not making a single post after completing computations. I have stopped now. ... The second (CP-10) is 16 times larger with gaps 28 and 2: 87873432313...
As expected, my idea proposed below is not new. David Broadhurst and Phil Carmody (both missed members of this list, unlike the Goldbach-proving spammers)...
Hi All! Could someone out there explain to me in simple terms, why, with all your research into prime numbers, it is not possible to prove When y = ( 2,3,4...)...
In a message dated 05/02/2005 08:12:13 GMT Standard Time, bobgillson@... writes: Could someone out there explain to me in simple terms, why, with all...
... Of course, I should have done a bit more thinking and less experimentation before posting, as I'm sure you have realized by now. If y^2-x^2 = p*q, where y...
... One snag: y^2-x^2 = (y-x)*(y+x) is a product of 2 primes if and only if (y-x and y+x are both primes) _or_ (y-x=1 and y+x is a product of 2 primes) The...
Hello primehunters, after long time today, I have found a new 9-tuplet. The record is: 90421624808713.300#+103498931 + 0,2,6,8,12,18,20,26,30 More 8-tuplets...
... Congratulations! It is also the largest known case of 9 simultaneous primes. http://hjem.get2net.dk/jka/math/simultprime.htm has been updated. -- Jens...
Fermat realized this 300 years earlier. And, this is the basis of his factoring algorithm. Milton L. Brown miltbrown at earthlink.net ... conjecture is ... ...
Milton Brown
miltbrown@...
Feb 7, 2005 11:31 am
16038
There seem to be a lot of conjectures/open questions regarding the existence of certain collections of primes (e.g. tuplets or arithmetic progressions) or the...
... The Riemann hypothesis. If you also consider computational number theory, then settling down whether P == NP would be equally, if not more important. ...
Christ van Willegen has found the largest known 14-tuplet: 26093748*67# + 383123187762431 + 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 Congratulations...
http://primes.utm.edu/top20/page.php?id=2 " Around 1825 Sophie Germain proved that the first case of Fermat's Last Theorem is true for such primes. Soon after...
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