Chance of ESP Prime Table

237%. You made my day. I could agree that correct formula is long and boring to write, so it could be better not to include these totals at all. But plain summing of probabilities is an ugliest error.

Toshio, maximum possible probability is 1, or 100%. There are some formulas how to combine probabilities of events with "or" or "and" conditions, you cannot just add or subtract them.

Ok, with some help from Excel...

Clearly, "the odds of finding a prime" can not exceed 100% or 1.00.

Roger's calculations, however, are not "the odds of finding a prime". Those numbers are "the expected number of primes". That IS a number that can exceed 1.00. (That's assuming we don't stop searching a K after a prime is found, of course.)

That's also why it's appropriate to add the numbers together rather than averaging them.

If, for example, we can expect to find 2 primes while searching K1, and 3 primes while searching K2, then clearly if we search both K1 and K2 we can expect to find 5 primes (not 2.5 primes.)


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My lucky number is 75898⁵²⁴²⁸⁸+1

Toshio, maximum possible probability is 1, or 100%. There are some formulas how to combine probabilities of events with "or" or "and" conditions, you cannot just add or subtract them.

Ok, with some help from Excel...

+---------------+-------+-------+-------+-------+-------+-------+ | k remaining | 5-6M | 6-7M | 7-8M | 8-9M | 9-10M | Total | +---------------+-------+-------+-------+-------+-------+-------+ | 91549 | 3.43% | 2.90% | 2.51% | 2.21% | 1.98% |12,37% | | 99739 | 5.25% | 4.44% | 3.85% | 3.39% | 3.03% |18,44% | | 131179 | 5.19% | 4.38% | 3.80% | 3.35% | 3.00% |18,24% | | 161041 | 6.57% | 5.55% | 4.81% | 4.24% | 3.80% |22,62% | | 163187 | 3.96% | 3.34% | 2.90% | 2.56% | 2.29% |14,18% | | 193997 | 2.96% | 2.50% | 2.17% | 1.91% | 1.71% |10,76% | | 200749 | 4.70% | 3.97% | 3.44% | 3.03% | 2.71% |16,63% | | 202705 |12.75% |10.78% | 9.34% | 8.24% | 7.37% |40,01% | | 209611 | 3.03% | 2.56% | 2.22% | 1.96% | 1.75% |11,01% | | 227723 | 4.72% | 3.99% | 3.46% | 3.05% | 2.73% |16,72% | | 229673 | 2.33% | 1.97% | 1.71% | 1.50% | 1.35% | 8,55% | | 238411 | 7.58% | 6.41% | 5.55% | 4.90% | 4.38% |25,71% | +---------------+-------+-------+-------+-------+-------+-------+ | Total | 47,62%| 41,92%| 37,45%| 33,79%| 30,80%|91,28% | +---------------+-------+-------+-------+-------+-------+-------+

The "Total" number on the right is a probability to find a prime for given k in whole search range (5-10M).
The "Total" number in the bottom is a probability to find any prime in given range (any k)
And the biggest bottom-right number is a probability that we'll find at least one prime during whole project. It's almost guaranteed!

Thanks Michael, I see you point now. Unfortunately, usage of word "chance" and percents in original post was very misleading. Treating these numbers as "density" of primes, final sum, being presented in form of 2.3744, makes sense - meaning that it is expected to be 2 or 3 primes within the whole search range for all k's.