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20210918, 23:29  #1  
Mar 2021
2^{2}·11 Posts 
3x a mersenne prime seems to have a prime nearby by less than twice the mersenne number
I noticed this and wondered if anyone has ever went on this path to find a large prime to put in the database. I haven't bought my rig yet to start working on the project for mersennes, but will soon and was just curious about this one as it seems fun to try maybe. Probably not enough cpu power for the is_prime tests, heh.
Quote:
Last fiddled with by LarsNet on 20210918 at 23:32 

20210918, 23:44  #2 
Mar 2021
2^{2}×11 Posts 
Since i posted something not so useful,i thought i'd share something interesting ( nothing new, just something old and interesting):
If you run any mersenne number in the following equation, you will always get a bin of repeating 1's and 0's. Code:
In [2521]: bin((2**1071)*((2**1071)//3)1) Out[2521]: '0b101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010100110101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101' Code:
In [2566]: p2ecm(8776024305713098891493168973639202693241257950045759271192581461) Out[2566]: [643, 84115747449047881488635567801, 162259276829213363391578010288127] 162259276829213363391578010288127//3+1 = 643 * 84115747449047881488635567801 In [2567]: bin(8776024305713098891493168973639202693241257950045759271192581461) Out[2567]: '0b101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101' Ok HERE we go: Code:
In [1615]: bin((2**1071)*((2**1071)//3+1)) Out[1615]: '0b101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101' meaning map 1 to 5 through 9 and 0 to 0 through 4, use this equation: Code:
a = 2**611 # 2305843009213693951 z = a + a z = int(str(z),16) h = (int(str(a), 16) + int(str(a), 16)) print(hex((zh)//6) 2305843009213693951 0001100001000110110 Last fiddled with by retina on 20210919 at 05:36 Reason: Long lines are long 
20210919, 04:32  #3 
"Alexander"
Nov 2008
The Alamo City
2×379 Posts 
Can a mod please get some [CODE] tags in that post? It overflowed my screen width, and I'm sure I wasn't the only one.

20210919, 11:36  #4 
Romulan Interpreter
Jun 2011
Thailand
2630_{16} Posts 
wow, you just discovered that if you take a number which is 1111...111 in binary and multiply it with about a third of it, you get 101010... Now, think about it viceversa, take any binary number which is a string of 1 (it can also be a string of 1 in any base) and divide it by 3 (which is binary is 11, but if you use other base, take 11 in that base, for example, in base ten, take eleven), and do the school division, with pencil and paper. What do you see?

20210919, 14:08  #5  
Feb 2017
Nowhere
4982_{10} Posts 
Quote:


20210921, 01:10  #6 
Mar 2021
2C_{16} Posts 
Yes, i'm a newbie, but i love what i've discovered and have a love for prime numbers and would like to help with the project if any of you have any ideas on what i can buy to contribute (while not much, but enough i hope (5 to 7k)) i would like to help: https://www.mersenneforum.org/showthread.php?t=27150

20210921, 03:16  #7 
"Curtis"
Feb 2005
Riverside, CA
1383_{16} Posts 
Is your interest Mersennes only, primes of some other forms, or factoring too? Those are the three main categories this forum's users work on.
If you're searching for primes, the best bangforbuck isn't a massive $5k machine; it's a gamingclass machine with fast memory, and if a GPU can be found at reasonable price then the GPU can do perhaps more work than all the cores of the CPU (depending on how nice a GPU one can locate, of course). GPU software is best cut out for Mersenne work, while the CPU can search for Mersennes too, or other primes of smaller size, or yet other projects around here. 
20210922, 20:58  #8  
Mar 2021
2^{2}·11 Posts 
Quote:
I do have a speedy Core I7 laptop that i could use for this project, an MSI Creator 17 A10SGS252 which has : Creator 17 A10SGS252 CPU Core i710875H; 2.3  5.1GHz GPU NVIDIA GeForce RTX2080 Super MaxQ Is that good enough a machine? BTW, i bought Elementary Number Theory: Primes, Congruences, and Secrets by William Stein to help me understand some of the material regarding nfs/gnfs. If anyone has any other recommendations, i'd love to hear it. (I'm struggling with putting the concept of ideals into code ) Last fiddled with by LarsNet on 20210922 at 21:17 

20210922, 21:21  #9 
"Curtis"
Feb 2005
Riverside, CA
3^{3}·5·37 Posts 
"good enough" is a matter of your level of patience. The only limitation that machine has other than "time spent to get a result" is that RAM installed limits the maximum size of NFS job you can run. An 8GB machine tops out around GNFS165 if running msieve + GGNFS, and more like GNFS 150 digits if running CADO. 16GB gets you about 15 digits larger capacity, though by that size your patience likely limits you as much as memory capacity.
For any other task run on this forum, your machine is fine it may take twice as long, but so what? If your interests get varied or intense enough to want to be able to run more tasks (or run tasks more quickly), then you know it's time to acquire a faster machine. 
20210922, 21:43  #10  
Mar 2021
2^{2}×11 Posts 
Quote:


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