... If we let span(x) to be defined for all natural numbers as the smaller of the "gaps" between this number and the previous or next prime, it'd be trivial to...
21226
Kermit Rose
kermit1941
Dec 30, 2009 3:47 am
... The factorial construction of proving a long gap is symmetric. If p is prime, then p# + 2, P# + 3, ...... up to p# + (p+1) are necessarily composite. and...
21225
rupert.wood@...
rupert.wood...
Dec 30, 2009 3:42 am
... Thank you David! I have downloaded Pari-GP and got an example of the above to work. If I want to compile/save a copy of a script like this for instant...
21224
djbroadhurst
Dec 30, 2009 2:22 am
... p = 397 seems to be the first prime for which this problem becomes hard, since in this case it appears that there is no "witness equation", as defined by...
21223
djbroadhurst
Dec 30, 2009 1:21 am
... My Pari-GP code was rather simple-minded: {wit(p)=local(f,g,m=1,s);s=sqrtint(p);forprime(q=2,s,m=m*q); ...
21222
rupert.wood@...
rupert.wood...
Dec 30, 2009 1:07 am
... That's most impressively quick! Can you please tell me how you found it? It would be very nice to have a piece of code to investigate later primes... ...
21221
rupert.wood@...
rupert.wood...
Dec 30, 2009 1:05 am
... That's most impressively quick! Could you please tell me how you found it? It would be really nice to have a piece of code that could be used to...
21220
djbroadhurst
Dec 30, 2009 12:51 am
... 337 = 2^7*5^2*7^2*11 - 3^3*13*17^3 David...
21219
rupert.wood@...
rupert.wood...
Dec 29, 2009 11:35 pm
Let P be a prime > 7, and let D={p1, p2, ..., pn} (n>1) be the set of all primes < sqrt(P). Consider a disjoint decomposition of the set D, say D = Q union R,...
21218
rupert.wood@...
rupert.wood...
Dec 29, 2009 8:56 pm
Thank you all for these contributions! {--- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" ... [Non-text portions of this message have been removed]...
21217
Peter Lesala
plesala@...
Dec 29, 2009 6:29 pm
Hi everyone, To increase the probability of finding prime numbers I find the strategy of using four different terms for the same integer constant very useful....
... See http://www.research.att.com/~njas/sequences/A023186 : "Lonely (or isolated) primes: increasing distance to nearest prime." It says: "Erdos and Suranyi...
21214
bill_jones92057
Dec 29, 2009 11:04 am
PI(N) ~= N /[ A*(LOG(N)^2) +B*LOG(N) +C, for N <= 10^23. This can be shown by a simple regression analysis of N/PI(N) vs LOG(N). This seems like a...
21213
Jaroslaw Wroblewski
jarek372000
Dec 29, 2009 9:32 am
This nice idea can be fixed as follows: For primes p<q take a = p# * q b = p# *k +1 chosen so that b-2=p#*k-1 is divisible by q. Then a*n+b-2 is always...
21212
djbroadhurst
Dec 29, 2009 9:08 am
... Perhaps this can be shown by arguments such as in MR0223298 (36 #6346) Jarden, Dov; Jarden, Moshe Simultaneous prime and composite members in two...
21211
rupert.wood@...
rupert.wood...
Dec 29, 2009 4:39 am
This notion is derived from the familiar prime gaps: The "span" of a prime is the smaller of the two gaps adjacent to it. For example, span(839) is...
21210
djbroadhurst
Dec 28, 2009 10:49 pm
... Noting the counterexamples for N = 125 and N = 126 that Jack has given, I remark on the more general problem of proving that, for some fixed theta, there...
21209
Jack Brennen
jbrennen
Dec 27, 2009 10:35 am
And even if he meant to be inclusive of N, such that 11 is considered to be between 11 and 11-sqrt(11), you are still left with N=125 and N=126, both of which...
21208
Bernardo Boncompagni
redgolpe
Dec 27, 2009 8:23 am
... There is no prime between 11 and 11-sqrt(11)=7.68 Bernardo Boncompagni ________________________________________________ p(25235715) is prime (Sep 2009). ...
21207
ronaldpeterdwyer
ronaldpeterd...
Dec 27, 2009 4:24 am
I'm going to put forth a conjecture, though somewhat similiar to other conjectures and theorems, I haven't seen stated before. For any positive integer N>3,...
21206
Kermit Rose
kermit1941
Dec 24, 2009 7:42 pm
The multi-polynomial part of the multi-polynomial quadratic sieve. Hello Prime number friends. I've worked out this part of the multiple polynomial quadratic...
21205
Harvey D Norris
harvich
Dec 24, 2009 12:59 am
Sat Jan 3, 2009 10:43 pm I went to solve the same puzzle as he when the realization of magic cubes occurred. I was drawing it out at Waylon's Tavern spare time...
21204
Harvey D Norris
harvich
Dec 24, 2009 12:18 am
It is noted that a squaring is not the same as a squire. Some say a squire is the attendant to the knight. And is known by the knight the pattern of its...
21203
djbroadhurst
Dec 23, 2009 8:22 pm
... I learnt to count like that in Chi-Nyanja: modzi : one wiri : two tatu : three nai : four sanu :...
21202
Paul Leyland
xilmanuk
Dec 23, 2009 5:22 pm
... Sorry for the late response to this thread but I've been rather tied up with Real Life(tm) recently. There is a persuasive suggestion that the divisibility...
21201
kraDen
kradenken
Dec 22, 2009 1:16 am
Hi All, Since the demise of Geocities the multifactorial search has been homeless. Now thanks to the kindness of the people at Free-DC (Special thanks to Phil...
21200
Harvey Norris
harvich
Dec 21, 2009 6:28 pm
I was looking for a yahoo group on mathematics that might solve some of my mathematical suppositions. I dont know how strict the moderator is as some of my...
21199
International Journal...
eic_iji
Dec 19, 2009 1:01 pm
International Journal of Mathematics and Computation (IJMC). ISSN 0974-570X (Online); ISSN 0974-5718 (Print) http://ceser.res.in/ijmc.html ...
21198
maximilian_hasler
maximilian_h...
Dec 16, 2009 2:01 pm
... The web page contains 9 times the word "formula" and 4 times the word "Formel", but only 3 or 4 "=" signs. It would be easier to understand and/or find an...
