Repdigit prime project

jasong · 2007-08-11, 03:56

A repdigit prime is a prime where most of the digits are the same number. For instance, if we set n at 43 and k at 3, possible repdigit primes would be 433, 4333, 43333.

Just like with Seventeen or Bust, Riesel Sieve, and the Prime Sierpinski Project, there are n-values for each k-value for which the combination will never, EVER yield a prime. The trick is to find a prime for every lower combination, so as to prove it. That is the reason I've started this thread. I'll list the unproven numbers, and if people want to attempt them, they may reserve them for their computer.

The original website, which I believe is abandoned is below.

http://www.freewebs.com/dries5/Prime_problems.htm

Form Smallest Proven n Remaining n Lower bound of k
1111...n 221 {3,7,11,13} Solved

2222...n 187 {3,7,11,13} Solved

3333...n 707 {7,11,13,37} Solved

4444...n 407 {3,7,11,37} Solved

5555...n 451 {3,7,11,13} Solved

6666...n 22297 {7,11,13,37} 1859 36500
1919 20000
2051 Solved: Prime for 9664
2123 Solved: Prime for 2237
2321 Solved: Prime for 10953
3817 20000
5533 20000
8497 10043
9757 13533
10841 Solved: Prime for 24218
12359 Solved: Prime for 4104
16511 Solved: Prime for 12449
16687 Solved: Prime for 3653
16867 Solved: Prime for 4026
17083 30000
19063 Solved: Prime for 6685
20669 16750
22127 Solved: Prime for 4588

7777...n 4477 {3,11,37} 909 10000
1591 10000
2827 Solved: Prime for 4545
3223 Solved: Prime for 3303
3293 10000
3513 Solved: Prime for 3058

8888...n 121 {3,7,11,13} Solved

9999...n 14927 {7,11,13,37} 1177 Solved: Prime for 3527
2587 9137
2873 20000
8593 41000
8659 Solved: Prime for 5668
11791 6130
12263 5000
12901 Solved: Prime for 14024

n...1111 38(infinite covering set) Solved

n...3333 4070 {7,11,13,37} 410 14000
817 14800 Reserved
1166 14032 Reserved
2959 Solved: Probable Prime for 6763
3674 Solved: Prime for 16097
n...7777 891 {3,11,13,37} 480 Solved: Prime for 11330
851 Probable Prime for 28895
n...9999 ** 10175 {7,11,13,37} 1342 Solved: Prime for 29711
1802 40000
1934 40000
3355 Solved: Prime for 13323 Dries De Clercq
4015 Solved: Prime for 3647 Patrick Keller
4420 40000
4477 Solved: Prime for 4817 Patrick Keller
4499 Solved: Prime for 11957 Dries De Clercq
6587 Solved: Prime for 5846 Dries De Clercq
6664 40000
7018 40000
8578 40000

jasong · 2007-08-11, 03:58

6666...n n=1591 reserved (from 10,000)
6666...n n=3293 reserved (from 10,000)

jasong · 2007-08-11, 04:26

Instructions:

First, you need to download pfgw from here. I attempted to find the file somewhere where it wouldn't be necessary to give out an email address, but I failed. Sorry. :(

After you download pfgw, you need to make an ABC2 file. Because we're dealing with repdigit numbers, there are two basic lines to start your files with:

ABC2 n+(10^$a-1)*10^m*d/9 (if the digits are placed in front of n)

ABC2 n*10^$a+(10^$a-1)*d/9 (if the digits are placed behind n)

So if n was 43 the repdigit was 3, and it was placed behind n, the first line of your file would be(btw, d represents the repdigit number):

ABC2 43*10^$a+(10^$a-1)*3/9

If n was 43 and the repdigit 3 were placed before, the first line would be:

ABC2 43+(10^$a-1)*10^m*3/9 (m is the number of digits in the n-value you're searching)

After you generate that first line, you go to the next line. Now, you don't want to redo work, so you have to go back and note where the previous search ended. Let's say the number is listed as 10,000. This would be one of the values for $a(The dollar sign indicates that it is a numeric variable). So if we wanted to go from 10,000 to 20,000 we would put:
a: from 10000 to 20000

and the file would be all we would need. Actually, since we're basically expected to continue the number until we find a prime or we're sick of the search, you might as well put a really high number and just check for the string 'is prime' every once in a while.

to run the program, go to the directory and type 'pfgw -f input.txt' (pfgw is the program, -f tells it to attempt to find a small factor before doing a primality test, and the last entry should be the name of the input file. Note that if you stop the programs execution by clicking on the DOS box and pressing Ctrl-C, you can simply start from where you left off by typing the command again, rather than having to change the input file.

Edit: As it turns out, pfgw makes a special file for probable primes. Whether or not the results can be proven as actual primes depends on the size of resulting number and available computing power.

ValerieVonck · 2007-08-11, 14:30

going to try

2587 9137 to 10.000

Jasong, can you give me the 2 lines for the ABC2 file?

Thanks.
C.

jasong · 2007-08-11, 20:58

Quote:

Originally Posted by CedricVonck

going to try

2587 9137 to 10.000

Jasong, can you give me the 2 lines for the ABC2 file?

Thanks.
C.

Code:

ABC2 14927*10^$a+(10^$a-1)*5/9
a: from 9138 to 200000

going to 10,000 would take less than an hour. Just crunch until you find a prime or get sick of the search. If you find a prime, a text file called 'prime' will be created. I forget what that type of file looks like when it's created, so just copy and paste the contents to this thread. Also, if you want to quit before you find the prime, just note what power of ten it's at in the DOS window, and post that number minus 1.(So that people don't accidentally skip over a possible prime)

jasong · 2007-08-13, 05:03

Um, guys, I made an error. I found a PRP in a file called 'pfgw' in one of my directories.

So instead of looking for a file called 'prime' you should be looking for a file called 'pfgw'.

I apologize for this error.

Btw, here's the PRP: 3293+(10^26198-1)*(10^4)*2/3 which is basically 6 repeated 26197 times and then 3293.

ValerieVonck · 2007-08-14, 10:39

Thank you ... I will start cracking asap.

ValerieVonck · 2007-08-19, 14:23

14927 tested to 16000
Stopping the search.

nuggetprime · 2007-09-18, 13:40

Here's a big tip for you: activate the -f100 (or more) switch. So you save A LOT OF TIME! Reserving 9999....12263 to 20000.

jasong · 2007-09-19, 04:26

Form Smallest Proven n Remaining n Lower bound of k
1111...n 221 {3,7,11,13} Solved

2222...n 187 {3,7,11,13} Solved

3333...n 707 {7,11,13,37} Solved

4444...n 407 {3,7,11,37} Solved

5555...n 451 {3,7,11,13} Solved

6666...n 22297 {7,11,13,37}
1859 36500
1919 20000
2051 Solved: Prime for 9664
2123 Solved: Prime for 2237
2321 Solved: Prime for 10953
3817 20000
5533 20000
8497 10043
9757 13533
10841 Solved: Prime for 24218
12359 Solved: Prime for 4104
16511 Solved: Prime for 12449
16687 Solved: Prime for 3653
16867 Solved: Prime for 4026
17083 30000
19063 Solved: Prime for 6685
20669 16750
22127 Solved: Prime for 4588

7777...n 4477 {3,11,37} 909 10000
1591 10000 (reserved today)might be unreserved fairly quickly
2827 Solved: Prime for 4545
3223 Solved: Prime for 3303
3293 26197(prime)
3513 Solved: Prime for 3058

8888...n 121 {3,7,11,13} Solved

9999...n 14927 {7,11,13,37} 1177 Solved: Prime for 3527
2587 9137 (reserved by cedricvonck)last update 11 Aug
2873 20000
8593 41000
8659 Solved: Prime for 5668
11791 6130
12263 5000 (reserved by nuggetprime on
12901 Solved: Prime for 14024

n...1111 38(infinite covering set) Solved

n...3333 4070 {7,11,13,37} 410 14000
817 14800 open
1166 14032 open
2959 Solved: Probable Prime for 6763
3674 Solved: Prime for 16097
n...7777 891 {3,11,13,37}
480 Solved: Prime for 11330
851 Probable Prime for 28895
n...9999 ** 10175 {7,11,13,37} 1342 Solved: Prime for 29711
1802 40000
1934 40000
3355 Solved: Prime for 13323 Dries De Clercq
4015 Solved: Prime for 3647 Patrick Keller
4477 Solved: Prime for 4817 Patrick Keller
4499 Solved: Prime for 11957 Dries De Clercq
6587 Solved: Prime for 5846 Dries De Clercq
6664 40000
7018 40000
8578 40000

jasong · 2007-09-19, 17:42

Just as a note pfgw failed to successfully test: PRP: 1591+(10^43396-1)*10^4*7/9

Edit: and then, it immediately had a problem with PRP: 1591+(10^43420-1)*10^4*7/9 1/144251
(the very next number it had to test)

I'm unreserving the number and recommending people DO NOT trust Core 2 Duo results for pfgw.

2007-08-11, 03:56	#1
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	Repdigit prime project A repdigit prime is a prime where most of the digits are the same number. For instance, if we set n at 43 and k at 3, possible repdigit primes would be 433, 4333, 43333. Just like with Seventeen or Bust, Riesel Sieve, and the Prime Sierpinski Project, there are n-values for each k-value for which the combination will never, EVER yield a prime. The trick is to find a prime for every lower combination, so as to prove it. That is the reason I've started this thread. I'll list the unproven numbers, and if people want to attempt them, they may reserve them for their computer. The original website, which I believe is abandoned is below. http://www.freewebs.com/dries5/Prime_problems.htm Form Smallest Proven n Remaining n Lower bound of k 1111...n 221 {3,7,11,13} Solved 2222...n 187 {3,7,11,13} Solved 3333...n 707 {7,11,13,37} Solved 4444...n 407 {3,7,11,37} Solved 5555...n 451 {3,7,11,13} Solved 6666...n 22297 {7,11,13,37} 1859 36500 1919 20000 2051 Solved: Prime for 9664 2123 Solved: Prime for 2237 2321 Solved: Prime for 10953 3817 20000 5533 20000 8497 10043 9757 13533 10841 Solved: Prime for 24218 12359 Solved: Prime for 4104 16511 Solved: Prime for 12449 16687 Solved: Prime for 3653 16867 Solved: Prime for 4026 17083 30000 19063 Solved: Prime for 6685 20669 16750 22127 Solved: Prime for 4588 7777...n 4477 {3,11,37} 909 10000 1591 10000 2827 Solved: Prime for 4545 3223 Solved: Prime for 3303 3293 10000 3513 Solved: Prime for 3058 8888...n 121 {3,7,11,13} Solved 9999...n 14927 {7,11,13,37} 1177 Solved: Prime for 3527 2587 9137 2873 20000 8593 41000 8659 Solved: Prime for 5668 11791 6130 12263 5000 12901 Solved: Prime for 14024 n...1111 38(infinite covering set) Solved n...3333 4070 {7,11,13,37} 410 14000 817 14800 Reserved 1166 14032 Reserved 2959 Solved: Probable Prime for 6763 3674 Solved: Prime for 16097 n...7777 891 {3,11,13,37} 480 Solved: Prime for 11330 851 Probable Prime for 28895 n...9999 ** 10175 {7,11,13,37} 1342 Solved: Prime for 29711 1802 40000 1934 40000 3355 Solved: Prime for 13323 Dries De Clercq 4015 Solved: Prime for 3647 Patrick Keller 4420 40000 4477 Solved: Prime for 4817 Patrick Keller 4499 Solved: Prime for 11957 Dries De Clercq 6587 Solved: Prime for 5846 Dries De Clercq 6664 40000 7018 40000 8578 40000 Last fiddled with by jasong on 2007-08-11 at 04:05

2007-08-11, 03:58	#2
jasong "Jason Goatcher" Mar 2005 3×7×167 Posts	6666...n n=1591 reserved (from 10,000) 6666...n n=3293 reserved (from 10,000) Last fiddled with by jasong on 2007-08-11 at 04:27 Reason: stupid typo, I'm like a child in a candy store when I start a new project

2007-08-11, 04:26	#3
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	Instructions: First, you need to download pfgw from here. I attempted to find the file somewhere where it wouldn't be necessary to give out an email address, but I failed. Sorry. :( After you download pfgw, you need to make an ABC2 file. Because we're dealing with repdigit numbers, there are two basic lines to start your files with: ABC2 n+(10^$a-1)10^md/9 (if the digits are placed in front of n) ABC2 n10^$a+(10^$a-1)d/9 (if the digits are placed behind n) So if n was 43 the repdigit was 3, and it was placed behind n, the first line of your file would be(btw, d represents the repdigit number): ABC2 4310^$a+(10^$a-1)3/9 If n was 43 and the repdigit 3 were placed before, the first line would be: ABC2 43+(10^$a-1)10^m3/9 (m is the number of digits in the n-value you're searching) After you generate that first line, you go to the next line. Now, you don't want to redo work, so you have to go back and note where the previous search ended. Let's say the number is listed as 10,000. This would be one of the values for $a(The dollar sign indicates that it is a numeric variable). So if we wanted to go from 10,000 to 20,000 we would put: a: from 10000 to 20000 and the file would be all we would need. Actually, since we're basically expected to continue the number until we find a prime or we're sick of the search, you might as well put a really high number and just check for the string 'is prime' every once in a while. to run the program, go to the directory and type 'pfgw -f input.txt' (pfgw is the program, -f tells it to attempt to find a small factor before doing a primality test, and the last entry should be the name of the input file. Note that if you stop the programs execution by clicking on the DOS box and pressing Ctrl-C, you can simply start from where you left off by typing the command again, rather than having to change the input file. Edit: As it turns out, pfgw makes a special file for probable primes. Whether or not the results can be proven as actual primes depends on the size of resulting number and available computing power. Last fiddled with by jasong on 2007-08-11 at 05:20

2007-08-11, 14:30	#4
ValerieVonck Mar 2004 Belgium 5·13² Posts	going to try 2587 9137 to 10.000 Jasong, can you give me the 2 lines for the ABC2 file? Thanks. C. Last fiddled with by ValerieVonck on 2007-08-11 at 14:32

2007-08-13, 05:03	#6
jasong "Jason Goatcher" Mar 2005 3×7×167 Posts	Um, guys, I made an error. I found a PRP in a file called 'pfgw' in one of my directories. So instead of looking for a file called 'prime' you should be looking for a file called 'pfgw'. I apologize for this error. Btw, here's the PRP: 3293+(10^26198-1)(10^4)2/3 which is basically 6 repeated 26197 times and then 3293. Last fiddled with by jasong on 2007-08-13 at 05:05

2007-08-14, 10:39	#7
ValerieVonck Mar 2004 Belgium 5·13² Posts	Thank you ... I will start cracking asap.

2007-08-19, 14:23	#8
ValerieVonck Mar 2004 Belgium 5·13² Posts	14927 tested to 16000 Stopping the search.

2007-09-18, 13:40	#9
nuggetprime Mar 2007 Austria 2·151 Posts	Big tip & reservation Here's a big tip for you: activate the -f100 (or more) switch. So you save A LOT OF TIME! Reserving 9999....12263 to 20000.

2007-09-19, 04:26	#10
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	Form Smallest Proven n Remaining n Lower bound of k 1111...n 221 {3,7,11,13} Solved 2222...n 187 {3,7,11,13} Solved 3333...n 707 {7,11,13,37} Solved 4444...n 407 {3,7,11,37} Solved 5555...n 451 {3,7,11,13} Solved 6666...n 22297 {7,11,13,37} 1859 36500 1919 20000 2051 Solved: Prime for 9664 2123 Solved: Prime for 2237 2321 Solved: Prime for 10953 3817 20000 5533 20000 8497 10043 9757 13533 10841 Solved: Prime for 24218 12359 Solved: Prime for 4104 16511 Solved: Prime for 12449 16687 Solved: Prime for 3653 16867 Solved: Prime for 4026 17083 30000 19063 Solved: Prime for 6685 20669 16750 22127 Solved: Prime for 4588 7777...n 4477 {3,11,37} 909 10000 1591 10000 (reserved today)might be unreserved fairly quickly 2827 Solved: Prime for 4545 3223 Solved: Prime for 3303 3293 26197(prime) 3513 Solved: Prime for 3058 8888...n 121 {3,7,11,13} Solved 9999...n 14927 {7,11,13,37} 1177 Solved: Prime for 3527 2587 9137 (reserved by cedricvonck)last update 11 Aug 2873 20000 8593 41000 8659 Solved: Prime for 5668 11791 6130 12263 5000 (reserved by nuggetprime on 12901 Solved: Prime for 14024 n...1111 38(infinite covering set) Solved n...3333 4070 {7,11,13,37} 410 14000 817 14800 open 1166 14032 open 2959 Solved: Probable Prime for 6763 3674 Solved: Prime for 16097 n...7777 891 {3,11,13,37} 480 Solved: Prime for 11330 851 Probable Prime for 28895 n...9999 ** 10175 {7,11,13,37} 1342 Solved: Prime for 29711 1802 40000 1934 40000 3355 Solved: Prime for 13323 Dries De Clercq 4015 Solved: Prime for 3647 Patrick Keller 4477 Solved: Prime for 4817 Patrick Keller 4499 Solved: Prime for 11957 Dries De Clercq 6587 Solved: Prime for 5846 Dries De Clercq 6664 40000 7018 40000 8578 40000

2007-09-19, 17:42	#11
jasong "Jason Goatcher" Mar 2005 3×7×167 Posts	Just as a note pfgw failed to successfully test: PRP: 1591+(10^43396-1)10^47/9 Edit: and then, it immediately had a problem with PRP: 1591+(10^43420-1)10^47/9 1/144251 (the very next number it had to test) I'm unreserving the number and recommending people DO NOT trust Core 2 Duo results for pfgw. Last fiddled with by jasong on 2007-09-19 at 17:45

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