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?

pretty bad for me
06738331905537__

[QUOTE=NBtarheel_33;342023]while FFFFFFFFFFFF is the farthest possible residue from a Mersenne prime.[/QUOTE]Would that not be 1 off, just like 0001?
Would not 8888888888888888 be furtherest from 000....000?

Excluding known-bad residues, my "closest" in the last 365 days is [URL="http://www.mersenne.org/report_exponent/?exp_lo=49330741&exp_hi=&B1=Get+status"]054A974FAF0241__[/URL] (the sorting at [url]http://www.mersenne.org/results/[/url] 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).

I Could see Chuck Curtis smugly posting 3 "000000000000" residue

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.

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.

[CODE]# pfgw -f0 -b2 -q"2^65536+2^32768+1"
2^65536+2^32768+1 is composite: RES64: [0000000000000000] [/CODE]

[QUOTE=kar_bon;342042]607815*2^17+1 is not prime. RES64: 00000000000002D9[/QUOTE]
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.

[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)[/CODE]

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)[/CODE]