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 Showing results 1 to 25 of 1000 Search took 0.36 seconds. Search: Posts Made By: paulunderwood
 Forum: Miscellaneous Math 2022-08-19, 19:23 Replies: 8 Views: 315 Posted By paulunderwood Summarizing the two cases: n%8=3 ::... Summarizing the two cases: n%8=3 :: 2^((n-1)/2) == -1 mod n :: z is even :: two solutions exist: z and z/2 n%8=7 :: 2^((n-1)/2 == 1 mod n :: z is odd :: one solution exists. Due to z being on...
 Forum: Miscellaneous Math 2022-08-19, 14:18 Replies: 8 Views: 315 Posted By paulunderwood On this theme, since n==3 mod 4 then n-1 is... On this theme, since n==3 mod 4 then n-1 is divisible by 2 and not 4. Then the only possible strengthening is a base 2 Euler PRP. That is up to multiplicative order, there seems to be one or two...
 Forum: Miscellaneous Math 2022-08-19, 04:47 Replies: 8 Views: 315 Posted By paulunderwood A small observation: If a number n==3 mod 4 is... A small observation: If a number n==3 mod 4 is Fermat 2-PRP then 2^(n-1)==1 mod n. If z is the multiplicative order of 2 mod n, then z divides n-1. Also (x+2^z) == x+1 mod n. Furthermore, (x+1)^(n+1)...
 Forum: Miscellaneous Math 2022-08-18, 15:26 Replies: 8 Views: 315 Posted By paulunderwood Recap: I am testing: Fermat 2-prp and... Recap: I am testing: Fermat 2-prp and (x+2^r)^(n+1)==4^r+1 where gcd(r,n-1)==1, and have reached n<4*10^14 without counterexample. Now, writing a=lift(Mod(2,n)^r) the Lucas part can be written as...
 2022-08-07, 17:52 Replies: 188 Views: 14,412 Posted By paulunderwood FactorDB has verified it. Now The Prime Pages... FactorDB has verified it. Now The Prime Pages awaits your submission under: Generalized Lucas number, Wagstaff, ECPP :smile:
 Forum: Linux 2022-08-03, 22:31 Replies: 10 Views: 686 Posted By paulunderwood I have never used screen before and am just... I have never used screen before and am just playing around with it now. It seems you want sudo crontab -e (or root's account) and enter there @reboot su math-user -c "cd /your/path && screen...
 2022-08-02, 23:31 Replies: 49 Views: 10,683 Posted By paulunderwood Nice one :tu: Nice one :tu:
 Forum: Linux 2022-08-02, 11:26 Replies: 10 Views: 686 Posted By paulunderwood I see this as two problems: Firstly getting... I see this as two problems: Firstly getting something to run at boot and secondly getting something to run when logging in. For the first use @reboot su math-user -c "X" (in sudo crontab -e) where...
 Forum: Linux 2022-07-31, 18:51 Replies: 10 Views: 686 Posted By paulunderwood I think you need to use screen as a @reboot cron... I think you need to use screen as a @reboot cron job. Details somebody please.
 Forum: Chess 2022-07-24, 20:30 Replies: 5 Views: 357 Posted By paulunderwood First Law of Robotics broken The first law of robotics (https://en.wikipedia.org/wiki/Three_Laws_of_Robotics) has been broken. A 7 year boy has been injured playing chess...
 Forum: sweety439 2022-07-22, 21:39 Replies: 13 Views: 560 Posted By paulunderwood Can't you stop asking all and sundry "Can you... Can't you stop asking all and sundry "Can you run...." or "Please factor...". If you persist, we mods will create a repository of such requests. You have hereby been warned.
 Forum: Riesel Prime Search 2022-07-22, 04:12 Replies: 1,984 Views: 249,553 Posted By paulunderwood 9473*2^4543680-1... 9473*2^4543680-1 (https://primes.utm.edu/primes/page.php?id=134201) (1367788 digits) found Vincent Diepeveen
 Forum: Proth Prime Search 2022-07-21, 14:42 Replies: 1 Views: 248 Posted By paulunderwood 6 million digits prime! Congrats to Ryan for 7*2^20267500 + 1 (https://primes.utm.edu/primes/page.php?id=134192) with 6,101,127 digits and entrance rank 17 in top5000. :banana: :banana: :banana: :banana: :banana:...
 Forum: science_man_88 2022-07-20, 20:46 Replies: 2 Views: 232 Posted By paulunderwood WB sm88. I never know if to use my or local,... WB sm88. I never know if to use my or local, but your code can be made better by: div(n,x)=local(tz=10^znorder(Mod(10,x)));if(n<=tz,return(n),return(n%tz+div(floor(n/tz),x))) I think znorder...
 Forum: Miscellaneous Math 2022-07-19, 18:03 Replies: 8 Views: 315 Posted By paulunderwood Let z=znorder(Mod(2,n)). Then... Let z=znorder(Mod(2,n)). Then [2^(z-r),-1;1,2^(z-r)]^(n+1) == 4^(z-r)+1 == (4^z+4^r)/(4^r) == (1+4^r)/4^r all mod n So 2^(r*(n+1))*[2^-r,-1;1,2^-r]^(n+1) = (1+4^r)*2^(r*(n-1)) mod n Or...
 Forum: Miscellaneous Math 2022-07-18, 23:48 Replies: 8 Views: 315 Posted By paulunderwood Rather than computing gcd(a^3-a,n)==1 I think... Rather than computing gcd(a^3-a,n)==1 I think gcd(r,(n-1)/2)==1 is better. Certainly verification testing is quicker (both over znorder). Note n divides 2^(n-1)-1. gcd(a^2-1,n)==1 ==>...
 Forum: Miscellaneous Math 2022-07-18, 18:26 Replies: 8 Views: 315 Posted By paulunderwood Finding a counterexample to this looks hopeless.... Finding a counterexample to this looks hopeless. Before my computer crashed under the heat of the day, it had reached 4e11. I suspect a counterexample at maybe 25 digits or more. Very much more for...
 Forum: Miscellaneous Math 2022-07-17, 20:34 Replies: 8 Views: 315 Posted By paulunderwood Answer: [n, a]=[79786523, 1056446] Now for a... Answer: [n, a]=[79786523, 1056446] Now for a harder problem: Let a = 2^r, so that the test becomes: {tst(n,r)=local(a=lift(Mod(2,n)^r)); n%4==3&& gcd(a^3-a,n)==1&& Mod(2,n)^(n-1)==1&&...
 Forum: Miscellaneous Math 2022-07-17, 16:29 Replies: 8 Views: 315 Posted By paulunderwood 3 mod 4 with free parameter Consider [a,-1;1,a] = 2*a + [-a,-1;1,-a] where M=[a,-1;1,a] has the character x^2-2*a*x+a^2+1 and its discriminant = -1. Solving the character gives x=a+-sqrt(-1), leading to a test: ...
 2022-07-17, 08:07 Replies: 49 Views: 10,683 Posted By paulunderwood I am now certifying revnumbpart(100031088) on a... I am now certifying revnumbpart(100031088) on a slow computer.
 Forum: Information & Answers 2022-07-16, 16:51 Replies: 16 Views: 510 Posted By paulunderwood Install lm-sensors, and run watch sensors and... Install lm-sensors, and run watch sensors and report back the respective temperatures.
 Forum: Information & Answers 2022-07-16, 15:24 Replies: 16 Views: 510 Posted By paulunderwood It is not unknown that sometimes a CPU needs... It is not unknown that sometimes a CPU needs reseating. This will also ensure you have perfect contact between the CPU and the heatsink, separted by the thinnest layer of paste when you reinstall the...
 2022-07-16, 07:01 Replies: 49 Views: 10,683 Posted By paulunderwood Using the following function to reverse the... Using the following function to reverse the digits of number of partitions: revnumbpart(n)=V=digits(numbpart(n));a=0;for(k=1,#V,a+=V[k]*10^(k-1));a; I get in seconds: ...
 Forum: sweety439 2022-07-15, 10:27 Replies: 13 Views: 560 Posted By paulunderwood Yet another thread hijacked with the same... Yet another thread hijacked with the same off-topic ramblings from sweety. Sweety, please confine your "studies" to your blog :rant:
 2022-07-14, 06:57 Replies: 49 Views: 10,683 Posted By paulunderwood You'll be enlightened soon. CM is is a joy with... You'll be enlightened soon. CM is is a joy with its MPI abilities. Like you say, a prime a day. It is so much fun in comparison to running Primo. Chuck is cutting back to one every 10 days :smile:
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