I was curious how many SGS tasks it takes to find a prime.
Since the numbers tested in SGS are virtually of the same size, dividing the number of tasks done by the number of primes found (in the current range, n=1290000) should be an approximation of the average number of tasks per prime found:
14362 tasks/prime

I haven't found a prime in the current range. So I asked myself is me not having found a prime expected (i.e. have I done fewer tasks than the 14362 needed on average) or am I overdue?

I have computed 25355 SGS tasks with a credit of 746124.09.
But since I have both crunched in the old range (n=666666) and the current (n=1290000), I first had to figure out how much of this work was done in the current range:
The old range gave 13.91 credit/WU and the current 39.91.
So it follows:
[tasks old range]*13.91 + [tasks current range]*39.91 = 746124.09
[tasks old range] + [tasks current range] = 25355
-> [tasks current range] ~ 15132

In conclusion, with approximately 15132 workunits done in the current range and an expected value of 14362, it is fair to say that I am slightely overdue for a prime or have I made a mistake somewhere?

Thanks Yves!

I played around with the Poisson distribution a little and assuming that average number of tasks/prime is 14362 and with Λ = tasks/14362 we get:

Unluckiest SGS crunchers:

Most tasks in the current range (n=1290000) with no primes (including DC) found:

Unluckiest SGS crunchers (part 2):

Second table includes those who've found primes but have more tasks (in the current range) than expected (based on number of primes [incl. DC] found):

Updated the stats, added a "tasks done since last update column" & removed those with 0 RAC.

On the flip side there are users like the latest SGS-prime discoverer Anto%* who found a prime after only ~2800 tasks.

To preempt the expected comments...: I'm not complaining, I congratulate her/him on her/his find; I'm merely remarking on the fact that lady luck seems to be generous to some and extremely withholding to others.

I think what you are missing here is a distribution of tasks per prime. A normal "bell curve" has few points on the edges and many points in the middle.

After 53,658 tasks the probability of having found at least one prime is ~97.61%
or in other words, the chance of having found no prime is ~2.39%.

No matter how many heads in a row come up, the chance of getting tails on the next flip of a coin is still 50%.

After 53,658 tasks the probability of having found at least one prime is ~97.61%

then it is not unreasonable to expect someone not getting a prime.

I don't know the numbers for PG... if the chance of not finding a prime in 54k tasks is 2.39% and if there are 1000 people who have crunched 54k tasks then I would expect that 24 of them would not have found a prime. If there are 2000 people in the cohort then I would expect 48 to not have found a prime.
____________
Werinbert is not prime... or PRPnet keeps telling me so.
Badge score: 12x3 + 1x4 + 2x6 + 2x7 + 1x8 + 1x9 + 1x10 = 93

Update: all users with 20,000+ tasks in the current range with no primes (incl. DC).
Includes a column for tasks done since last update (16 Feb 2022).

https://www.primegrid.com/workunit.php?wuid=781597568
Well, well. I am out of that list before even getting into that list. Took me ~17600 tasks.

https://www.primegrid.com/workunit.php?wuid=781597568
Well, well. I am out of that list before even getting into that list. Took me ~17600 tasks.

Congratulations!

I, on the other hand, am now at 42,500+ tasks and still nothing...
Gotta stay patient I guess.

I have done 515947 tasks with 35 primes (5 of those 2nds).
515947/30 = 17198

I wish you to find one soon!
It has to be soon!

#4 now with 46,466 tasks.

#3 vko (51,017)
#2 Jonathan Connaughty (52,141)
#1 wafflingdwarf (54,635)

Let's see if I can overtake them as well before finding (or dc'ing) a SGS prime.
Assuming of course that I will in fact eventually find one...

#3 ~ 51,069 tasks

#2 Jonathan Connaughty (52,141)
#1 wafflingdwarf (55,006)

#2 ~ 52,306 tasks

#1 wafflingdwarf (55,276)

Mmh, wafflingdwarf seems determined not to give up her/his #1 spot:

#2 ~ 56,022 tasks
#1 wafflingdwarf (57,198)

And the probabilities for wafflingdwarf (and me)

≥1 prime: 98.13% (97.97)
≥2 primes: 90.70% (90.07)
≥3 primes: 75.90% (74.66)
≥4 primes: 56.27% (54.65)

It's official, with ~ 58,713 tasks in the current range and no primes found (or dc'ed) I'm now the unluckiest SGS cruncher. wafflingdwarf is a close 2nd with 58,281 tasks.

However, the more salient point is that we've both done more than 58k tasks (>4*avg.) and still neither of us has found a prime. Isn't that mind-bogglingly unlucky?!

Updated probabilities:

≥1 prime: 98.32%
≥2 primes: 91.45%
≥3 primes: 77.42%
≥4 primes: 58.31%

It's official, with ~ 58,713 tasks in the current range and no primes found (or dc'ed) I'm now the unluckiest SGS cruncher. wafflingdwarf is a close 2nd with 58,281 tasks.

However, the more salient point is that we've both done more than 58k tasks (>4*avg.) and still neither of us has found a prime. Isn't that mind-bogglingly unlucky?!

Updated probabilities:

≥1 prime: 98.32%
≥2 primes: 91.45%
≥3 primes: 77.42%
≥4 primes: 58.31%

Isn't that mind-bogglingly unlucky?!

At a >1% chance it is not mind bogglingly unlucky, merely just unlucky.

At a >1% chance it is not mind bogglingly unlucky, merely just unlucky.

I'm not sure I understand what you're trying to say here.
It seems to me how one chooses to describe the severity of unluckiness would be wholly subjective. Unless there are universally recognized standard levels of degrees of unluckiness I'm not aware of.

Anyway, I'm now over 60k tasks (~60,058) with a probability ≥1 prime of 98.47%.
I will hit 99% at 66,105 tasks. So I guess I have a new goal :)

I finally found one, it was 'just' a DC, but still...
Hopefully now the curse is broken :)

Grave digging a thread here. I did a rush on SGS as it was falling off the t5k. I was actually trying to be the "unluckiest" back in 2018, i think i got to third with 35343 tasks when i finally got a dc prime.