Quote from: justusranvier on March 27, 2013, 01:21:04 PM

~~$1.00~~ 2011-04-16
~~$1.26~~ 2011-04-22
~~$1.58~~ 2011-04-26
~~$2.00~~ 2011-04-28
~~$2.51~~ 2011-11-29
~~$3.16~~ 2011-12-15
~~$3.98~~ 2011-12-25
~~$5.01~~ 2012-05-16
~~$6.31~~ 2012-06-19
~~$7.94~~ 2012-07-16
~~$10.00~~ 2012-09-02
~~$12.59~~ 2012-12-04
~~$15.85~~ 2013-01-21
~~$19.95~~ 2013-02-03
~~$25.12~~ 2013-02-13
~~$31.62~~ 2013-02-28
~~$39.81~~ 2013-03-06
~~$50.12~~ 2013-03-19
~~$63.10~~ 2013-03-24
~~$79.43~~ 2013-07-10
~~$100.00~~ 2013-07-29
$125.89
$158.49
$199.53
$251.19
$316.23
$398.11
$501.19
$630.96
$794.33
$1,000.00
$1,258.93
$1,584.89
$1,995.26
$2,511.89
$3,162.28
$3,981.07
$5,011.87
$6,309.57
$7,943.28
$10,000.00
$12,589.25
$15,848.93
$19,952.62
$25,118.86
$31,622.78
$39,810.72
$50,118.72
$63,095.73
$79,432.82
$100,000.00
$125,892.54
$158,489.32
$199,526.23
$251,188.64
$316,227.77
$398,107.17
$501,187.23
$630,957.34
$794,328.23
$1,000,000.00

The following are the intervals between the dates for the 0.1 increments of log_10 (Mt. Gox price in USD), supplied by the OP:

time from 0.0 to 0.1: 6 days
time from 0.1 to 0.2: 4 days
time from 0.2 to 0.3: 2 days
time from 0.3 to 0.4: 215 days
time from 0.4 to 0.5: 16 days
time from 0.5 to 0.6: 10 days
time from 0.6 to 0.7: 143 days
time from 0.7 to 0.8: 34 days
time from 0.8 to 0.9: 27 days
time from 0.9 to 1.0: 48 days
time from 1.0 to 1.1: 93 days
time from 1.1 to 1.2: 48 days
time from 1.2 to 1.3: 13 days
time from 1.3 to 1.4: 10 days
time from 1.4 to 1.5: 15 days
time from 1.5 to 1.6: 6 days
time from 1.6 to 1.7: 13 days
time from 1.7 to 1.8: 5 days
time from 1.8 to 1.9: 108 days
time from 1.9 to 2.0: 19 days

minimum: 2 days
maximum: 215 days
mean: 41.75 days
median: 15.5 days

Interestingly, the short (single digit intervals) exist at both the low and high price ends, indicating that the growth is quite a bit faster than linear (if the short intervals clustered at the low end and the long intervals clustered at the high end that would indicate closer to linear growth). Also, only three of the intervals are in the triple digits. Based on the mean and median that I calculated, one could reasonably extrapolate using a month as the interval (in other words, a ten fold increase every ten months). At that rate, we'd see:

08-13: 2.1
09-13: 2.2
10-13: 2.3
11-13: 2.4
12-13: 2.5
01-14: 2.6
02-14: 2.7
03-14: 2.8
04-14: 2.9
05-14: 2.9
06-14: 3.0 (1,000 USD!)
07-14: 3.1
08-14: 3.2
09-14: 3.3
10-14: 3.4
11-14: 3.5
12-14: 3.6
01-15: 3.7
02-15: 3.8
03-15: 3.9
04-15: 4.0 (10,000 USD!)
05-15: 4.1
06-15: 4.2
07-15: 4.3
08-15: 4.4
09-15: 4.5
10-15: 4.6
11-15: 4.7
12-15: 4.8
01-16: 4.9
02-16: 5.0 (100,000 USD!)
03-16: 5.1
04-16: 5.2
05-16: 5.3
06-16: 5.4
07-16: 5.5
08-16: 5.6
09-16: 5.7
10-16: 5.8
11-16: 5.9
12-16: 6.0 (1,000,000 USD!)

If you think that Bitcoin will largely replace fiat currencies, then it must reach at least one million USD. With all of the horrible economic news (massive national debts, governments seizing funds from bank accounts, the serious weakening of all fiat currencies, etc.) that has been going around since pretty much the turn of the millennium, I would not be surprised if this pattern holds, or even turns out to be too conservative (e.g., the milestones happen sooner than projected here).