There is a little table on here:

http://www.mersenne.org/various/math.php
I'll reproduce it here slightly edited:

Code:

Exponents Bit
up to depth
--------- -----
3960000 60
5160000 61
6515000 62
8250000 63
13380000 64
23390000 65
29690000 66
37800000 67
47450000 68
58520000 69
75670000 70
96830000 71

This relationship between log(exponent) and bit depth is roughly linear, with a bit of a kink around 64 and 65 bits.

If you plot the log of the exponent against the bit depth (log to base 2 of the trial factor to depth), you get a nice straight line from a bit depth of 65 onwards.

I added a trend line to that and the equation was this:

ln(E) = 0.2346*D + 1.7171

Where E is the exponent and D is the bit depth.

So using this, it's tentatively possible to extend the table, but whether or not this linear relationship should continue I don't know. Assuming it does, here's what the numbers would be:

Code:

Exponents Bit
up to depth
--------- -----
23390000 65
29690000 66
37800000 67
47450000 68
58520000 69
75670000 70
96830000 71
120640000 72
152530000 73
192860000 74
243860000 75
308340000 76
389860000 77
492940000 78
623280000 79
788070000 80
996440000 81
1259900000 82
1593020000 83
2014220000 84
2546790000 85
3220170000 86
4071590000 87

So it seems as though Operation Billion Digits should be taking numbers to 87 bits, and currently there are 10 (soon to be 13) exponents that are at 81 bits.

Also, the first lot of 100 million digit candidates should be trial factored to 77 bits.

Once again, I do not know if this linear relationship between exponent and trial factor depth should continue. So take it with a pinch of salt until someone who actually knows something about it makes a comment.