Well, the count can only be off by an integer. --ms On 23-Dec-15 16:15, Dan Asimov wrote:
Among numbers not divisible by any prime less than p, there should be exactly an asymptotic probability of 1/p that they are divisible by p.
But this seems to approach the asymptote very irregularly.
Frequent case in point: Numbers relatively prime to 2*3*5 = 30 that are divisible by 7.
Here are some statistics:
Up through 10 there is a fraction of 0.1000000000000000 numbers whose first prime factor is 7 among numbers relatively prime to 30.
Up through 100 there is a fraction of 0.1600000000000000 numbers whose first prime factor is 7 among numbers relatively prime to 30.
Up through 1000 there is a fraction of 0.1433962264150943 numbers whose first prime factor is 7 among numbers relatively prime to 30.
Up through 10000 there is a fraction of 0.1429643527204503 numbers whose first prime factor is 7 among numbers relatively prime to 30.
Up through 100000 there is a fraction of 0.1428464279017439 numbers whose first prime factor is 7 among numbers relatively prime to 30.
Up through 1000000 there is a fraction of 0.1428571428571428 numbers whose first prime factor is 7 among numbers relatively prime to 30.
Why the sudden huge accuracy at 1 million?
(It's a lot less accurate at 10 million.)
—Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun