i. Almost every positive integer is composite.
ii. Almost every prime has more than 1000 digits.

Are the above statements true?

Please comment.

(In reply to re(2): mostly a discussion by Charlie)

Another way to look at this is from a probabilistic perspective.  For sake of simplicity let us say that the time each one goes off is uniformly random from 0 to 10.

So now take any time 0<t<10 and consider the probability of a given timer going off within the last t minutes.  This is simply t/10, so for example if t=1 minute then we would expect a given timer to go off in the last minute with a probability of 10%.  Now if we take this times total number of timers we get the expected number of timers that will go off within that time, since the total number of clocks is infinite then the expected number is also infinite for any finite t.  So this can be seen as saying that no matter how close we get to the end of the 10 minutes there will always be an infinite number of timers left to go off and the "remaining" infinite timers will go off at exactly 10 minutes. 

Posted by Daniel on 2018-09-26 20:25:00