[XPM] Primecoin Record Books

[Lauda]

Nice!

[1713999204]

1713999204

[1713999204]

1713999204

[1713999204]

1713999204

[1713999204]

1713999204

[hashman]

You tested the centers, you need to test the chain results. In Sunny's paper it describes how to get them, or here:

http://en.wikipedia.org/wiki/Cunningham_chain

You are quite right. However, the first probable prime still fails.
The positive result is:

Code:

Primality testing 65004063504559525007738276505391185322137155270201199057971076511954045665048965173722209501026611156768988779138868408914387452650147975793533060274322762631 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 49.24% and helper 2.29% (150.19% proof)
65004063504559525007738276505391185322137155270201199057971076511954045665048965173722209501026611156768988779138868408914387452650147975793533060274322762631 is prime! (0.0250s+0.0033s)

does this mean it's not actually generating valid primes?

As I understand the primecoin paper, it accepts pseudoprimes for making a block..  as a true check of primality would take too long for nodes to verify.   

[Aggrophobia]

any new records?

[Clark]

It looks like block 1592 has enough digits to take second place on the CC9, 1st kind.

Block 1592: 1CC09, 125 digits

[rethaw]

This is the python script I'm using to poll for record breakers.

EDIT: Use Clark's script below.

[keenanpepper]

Has it been confirmed that these are valid prime chains? If I'm not mistaken (please correct me if I am), primecoin only checks for probable primality.

You're absolutely right. I'm in the process of checking all these primes with GMP-ECPP (http://gmp-ecpp.sourceforge.net/). I'd be really surprised if any were composite (because "probable prime" means 1 in a zillion chance of being composite), but it can't hurt to check. BTW, if anyone knows a faster primality certificate generator, I'd love to hear about it.

[achillez]

this is very cool

[Lauda]

Just ran those checks they aren't mine 

[keenanpepper]

The 9 numbers 1574643694870716234768119109262250640648052155467238286652911336545168633619161 6303820985251295842020684640523576306336183730859560 * 2^n + 1, 0 <= n <= 8 are all actually prime (according to GMP-ECPP).

Now onto the ones from block 5355...

[rabit]

The 9 numbers 1574643694870716234768119109262250640648052155467238286652911336545168633619161 6303820985251295842020684640523576306336183730859560 * 2^n + 1, 0 <= n <= 8 are all actually prime (according to GMP-ECPP).

Now onto the ones from block 5355...

I verified both chains using ECPP in MAGMA.

[Clark]

My Python code :-)

This needs to be updated to include the Twin Prime record lengths. I wan't able to decipher the Twin Prime records website for lengths, but there's not much modification required.

The code will run through the entire block chain on the first run then save the results to a text file. Subsequent runs will simply check all blocks since the previous run.

Note this code uses ServiceProxy, which is available from the Bitcoin wiki.

Edit: The chain code comes out in hexadecimal, so a 10-length chain is 1CC0a, for instance.

Code:

from jsonrpc import ServiceProxy

import time, json

USER = '<user>'
PASS = '<pass>'
PORT = 9912


fname = 'worldrecords.txt'

# Searching for new world records

def main():
	ip = '127.0.0.1'
	addy = 'http://%s:%s@%s:%i' % (USER,PASS,ip,PORT)
	p = ServiceProxy(addy)
	
	# http://users.cybercity.dk/~dsl522332/math/Cunningham_Chain_records.htm

	records = {
		'1CC06':633,
		'2CC06':475,
		'1CC07':356,
		'2CC07':251,
		'1CC08':186,
		'2CC08':224,
		'1CC09':185,
		'2CC09':111,
		'1CC0a':99,
		'2CC0a':109,
		'1CC0b':50,
		'2CC0b':63,
		'1CC0c':42,
		'2CC0c':62,
		'1CC0d':39,
		'2CC0d':33,
		'1CC0e':25,
		'2CC0e':33,
		'1CC0f':24,
		'2CC0f':32,
	}

	primecoin = {}

	data = {}

	try:
		with open(fname, 'r') as f:
			data = json.load(f)
	except:
		pass

	blk = 1

	if 'block' in data:
		blk = data['block']

	if 'records' in data:
		records = data['records']

	if 'primecoin' in data:
		primecoin = data['primecoin']

	info = p.getinfo()
	height = info['blocks']

	while blk <= height:
		hsh = p.getblockhash(blk)
		block = p.getblock(hsh)
		
		chain = block['primechain'].split('.')[0]
		chainlength = int(chain[3:5],16)
		origin = block['primeorigin']
		digits = len(origin)

		if chain in records:
			if digits > records[chain]:
				print('New World Record!\n Block %i, Chain %s, %i digits (previously %i digits)\n' % 
					(blk, chain, digits, records[chain]))
				records[chain] = digits
				primecoin[chain] = digits
		else:
			if chain not in primecoin:
				primecoin[chain] = digits
				print('New Chain Type: %s, Block %i, %i digits' % (chain, blk, digits))
			elif digits > primecoin[chain]:
				primecoin[chain] = digits
				print('New Primecoin record: %s, %i digits, Block %i' % 
					(chain, digits, blk))

		blk += 1

	data = {
		'records': records,
		'primecoin': primecoin,
		'block': blk
	}

	with open(fname, 'w') as f:
		json.dump(data, f)

	print('\n\nCurrent Records')
	for chain in records:
		print(' %s: %4i' % (chain, records[chain]))

	print('\n\nPrimecoin Records')
	for chain in primecoin:
		print(' %s: %4i' % (chain, primecoin[chain]))

if __name__ == '__main__':
	main()

[Clark]

We found our first length-10 chain at block 17937, type 1CC0a, 86 digits. Then we bested it at Block 21362, 96 digits.

World record is 99 digits, but both of these chains are good enough to knock out the existing 2nd and 3rd place chains on the books:

Code:

CC10, 1st kind:
---------------
1324846487162*223#-1, 99 digits, 05/09, Augustin(NewPGen/PFGW)
3462418*151#+5286829397849, 66 digits, 05/04, Alm/Andersen(Primo)
9440733252109*127#-1, 62 digits, 11/08, Augustin(NewPGen/PFGW)

[RandyFolds]

We found our first length-10 chain at block 17937, type 1CC0a, 86 digits. Then we bested it at Block 21362, 96 digits.

World record is 99 digits, but both of these chains are good enough to knock out the existing 2nd and 3rd place chains on the books:

Code:

CC10, 1st kind:
---------------
1324846487162*223#-1, 99 digits, 05/09, Augustin(NewPGen/PFGW)
3462418*151#+5286829397849, 66 digits, 05/04, Alm/Andersen(Primo)
9440733252109*127#-1, 62 digits, 11/08, Augustin(NewPGen/PFGW)

Now that...that is friggin' rad.

[Lauda]

We found our first length-10 chain at block 17937, type 1CC0a, 86 digits. Then we bested it at Block 21362, 96 digits.

World record is 99 digits, but both of these chains are good enough to knock out the existing 2nd and 3rd place chains on the books:

Code:

CC10, 1st kind:
---------------
1324846487162*223#-1, 99 digits, 05/09, Augustin(NewPGen/PFGW)
3462418*151#+5286829397849, 66 digits, 05/04, Alm/Andersen(Primo)
9440733252109*127#-1, 62 digits, 11/08, Augustin(NewPGen/PFGW)

Lol nice.
Soon world record?

[Koooooj]

If I am not mistaken, Block 12344 contains a notable bi-twin chain.  The origin is 107 digits long and it is a chain of 3 links (i.e. 8 primes).  It is not a world record, but would be 4th on the list of chains of 3 links.  I was the miner of this block and would be willing to demonstrate ownership of the coins.

Edit:  It would appear that block 17302 also contains a (somewhat less) notable bi-twin chain.  It is only 97 digits long, but also contains 3 links.  As with the other, I am the miner and would be willing to show ownership.

[AgentME]

If I am not mistaken, Block 12344 contains a notable bi-twin chain.  The origin is 107 digits long and it is a chain of 3 links (i.e. 8 primes).  It is not a world record, but would be 4th on the list of chains of 3 links.  I was the miner of this block and would be willing to demonstrate ownership of the coins.

You can verify you own an address with the signmessage command:

Code:

primecoind signmessage addresshere "Koooooj owns this address"

and posting the address, message, and signature.

(I think you could run that in the debug console too, just omit the primecoind part at the start. Or is there just a UI to this feature? I'm not using the QT client.)

[r3wt]

this is all very cool, but i fail to see the need for prime numbers this large, other than so you can brag about the record to your fellow nerds of course.

[AgentME]

this is all very cool, but i fail to see the need for prime numbers this large, other than so you can brag about the record to your fellow nerds of course.

(These aren't particularly large for prime numbers. They're big  for prime number chains.) Some mathematicians may find this data useful. That's already infinitely more valuable than the results of bitcoin's sha256 / litecoin's scrypt random proof-of-work statements outside of the context of the currency.

[r3wt]

this is all very cool, but i fail to see the need for prime numbers this large, other than so you can brag about the record to your fellow nerds of course.

(These aren't particularly large for prime numbers. They're big  for prime number chains.) Some mathematicians may find this data useful. That's already infinitely more valuable than the results of bitcoin's sha256 / litecoin's scrypt random proof-of-work statements outside of the context of the currency.

good point, however i disagree that they are "infinitely more valuable". XPM(prime) has scientific value(which in my mind is debatable, but then again i'm no mathematician) and sha and scrypt has security(proven until its broken) seems like an apples and oranges argument to me.

[Koooooj]

For block 12344:

Code:

20:58:10
signmessage APLLrWbHapoRVxLAxBUkDU1hkx4VbCJHQX "Koooooj owns this address"

20:58:10
IBBD3qd/bbh5npcj7pEQCBqZUwiYaaE/y097+P0EBeB5fH4eJCqvNzrxzm20P6kWFq/0wmp0cZQTHk78cpfaYbM=

For block 17302:

Code:

21:00:27
signmessage AbrPM2J3WLvgz87t13wU46VwvVW5dM1Vdq "Koooooj owns this address"

21:00:27
IH8dQ+I2e4WWZIpXbqhXrquLXMnNdx847+HUeuadcqyeB77XPe3tmN2bG/FdOPZv7id9Q0eMuQ4UO7iBaq0wUf0=

I think I got the right blocks and signed correctly; my local QT client returns true upon verification requests.