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Old 2013-05-30, 21:09   #1
NBtarheel_33
 
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Default How close have you been to finding a Mersenne prime?

Define "close" in the following manner: a residue of 000000000001 is the closest possible residue to a Mersenne prime, while FFFFFFFFFFFF is the farthest possible residue from a Mersenne prime.

Given this definition, what is the closest/farthest you have personally been from discovering a new Mersenne prime? How about GIMPS as a whole?
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Old 2013-05-30, 21:52   #2
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pretty bad for me
06738331905537__
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Old 2013-05-30, 22:22   #3
Uncwilly
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Quote:
Originally Posted by NBtarheel_33 View Post
while FFFFFFFFFFFF is the farthest possible residue from a Mersenne prime.
Would that not be 1 off, just like 0001?
Would not 8888888888888888 be furtherest from 000....000?
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Old 2013-05-30, 22:25   #4
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Excluding known-bad residues, my "closest" in the last 365 days is 054A974FAF0241__ (the sorting at http://www.mersenne.org/results/ makes this easy to find).

I think the definition should be such that 000000000001 and FFFFFFFFFFFF are equally close - they're each just 1 apart from showing all zeroes in the 64-bit residue. In other words: the "closest" residue is the one that is closest to 0 mod 2^64.

If we drop the "Mersenne" restriction and I look at my PRPnet log files, my closest is: 0000083778FDEA40 on 507292*40^20317+1. I've run enough tests on even smaller numbers that I might have closer ones out there, but not in log files that are at hand (or exist at all).
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Old 2013-05-30, 22:33   #5
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I Could see Chuck Curtis smugly posting 3 "000000000000" residue
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Old 2013-05-30, 23:00   #6
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1881*2^774126-1 is not prime. Res64: 00000F12ABCED83E
1745*2^872506-1 is not prime. Res64: 00000E6B7FE01929
797*2^1088860-1 is not prime. Res64: 00000C48959C0818
1471*2^944575-1 is not prime. Res64: 000008C5C489296D
333*2^1194794-1 is not prime. Res64: 0000085458B0E7B9
3645*2^21+1 is not prime. Proth RES64: 000000015B5CADFD
108045*2^18+1 is not prime. Proth RES64: 00000004206C33F6
651358155*2^13+1 is not prime. RES64: 0000000000081BF1
607815*2^17+1 is not prime. RES64: 00000000000002D9

and many other examples like these.
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Old 2013-05-30, 23:40   #7
CRGreathouse
 
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So many ways to measure distance!

Linearly, from 000...0 to FFF...F? Circularly, with FFF...F being just as near as 000...1? Digit-wise, so 100...0 and 000...1 are equally far? By digits but circularly? Etc.
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Old 2013-05-30, 23:52   #8
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Code:
# pfgw -f0 -b2 -q"2^65536+2^32768+1"
2^65536+2^32768+1 is composite: RES64: [0000000000000000]
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Old 2013-05-31, 00:04   #9
henryzz
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Quote:
Originally Posted by kar_bon View Post
607815*2^17+1 is not prime. RES64: 00000000000002D9
0x2D9=729=3^6
This implies I believe(assuming that the residue being 2D9 wasn't a fluke)(607815*2^17+1)/(6+1) is 3-PRP(In reality it is prime).

There are probably more similar examples in your list. It would be nice if we could harness this to find prps.
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Old 2013-05-31, 00:12   #10
chalsall
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Code:
mysql> select Exponent.Exponent,Users.DisplayName,Assigned.FactFrom,Assigned.FactTo from Assigned,Exponent,Users where Assigned.Exponent=Exponent.Exponent and Exponent.Status=1 and Assigned.User=Users.User;
+----------+---------------+----------+--------+
| Exponent | DisplayName   | FactFrom | FactTo |
+----------+---------------+----------+--------+
| 57885161 | Jerry Hallett |       72 |     73 | 
+----------+---------------+----------+--------+
1 row in set (0.00 sec)
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Old 2013-05-31, 00:37   #11
chalsall
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But, to be fair, it was close...

Code:
mysql> select Exponent.Exponent,Users.DisplayName,Assigned.FactFrom,Assigned.FactTo from Assigned,Exponent,Users where Assigned.Exponent=Exponent.Exponent and Exponent.Exponent>=57884571 and Exponent.Exponent<=57885257 and Assigned.User=Users.User and Assigned.WorkType=1;
+----------+---------------+----------+--------+
| Exponent | DisplayName   | FactFrom | FactTo |
+----------+---------------+----------+--------+
| 57884647 | KyleAskine    |       72 |     73 | 
| 57884747 | Bdot          |       72 |     73 | 
| 57884891 | Jerry Hallett |       72 |     73 | 
| 57885143 | Bdot          |       72 |     73 | 
| 57885161 | Jerry Hallett |       72 |     73 | 
| 57885167 | Bdot          |       72 |     73 | 
| 57885209 | KyleAskine    |       72 |     73 | 
| 57885211 | KyleAskine    |       72 |     73 | 
| 57885257 | KyleAskine    |       72 |     73 | 
+----------+---------------+----------+--------+
9 rows in set (0.01 sec)
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