As they say, “A couple of months in the laboratory can frequently save a couple of hours in the library.” Or in this case, a thousand-plus hours of computer time saved a few minutes of looking it up (https://en.wikipedia.org/w/index.php?title=Prime_number&oldi...) or asking a mathematician.
Curiously, all the material out there today can cause a sort of paralysis.
Similar to how we used to argue and banter and have fun about factual disagreements at the bar, while today we can take our phones and look it up (upsides are obvious of course) sucking out part of the fun.
Now if you have some faily simple question today and Google it, you'll find tons of adjacent advice, articles, perhaps even a community dedicated to that sort of thing, libraries etc. Now you either deliberately shut it all out and go ahead with your project, explicitly ignoring all the above, or you start learning it, standing on the shoulders of giants etc.
It can be kind of discouraging to see how much you don't know but is out there, while in the 80s and 90s people had no choice but to rediscover lots of stuff on their own and feel as if they had actually invented the thing, simply due to a lack of Google and Wikipedia.
But overall it's no reason to give up, there is always stuff at the edges to look into, we just have to climb the tree a bit more because the low hanging fruit is gone. Or just pretend we live pre-Google and program away, without checking the answer first. Your boss may not like this latter strategy though.
Obviously Wikipedia didn't exist in 1994; I only gave the link for someone who is actually interested in looking it up today. A paper clearly explaining how to compute π(x) (I was just reading it) had come out in 1985: https://www.ams.org/journals/mcom/1985-44-170/S0025-5718-198...
Where would the average bloke in the street go to find that in 1994? And where would they get that knowledge?
(I mean, these days, the first thing you'd do is Google, the second thing is ask on SO or similar. You'd do this before even thinking about coding something yourself. So the bar to jumping to brute force has shifted somewhat.)
(I'd love to live in a town where the average bloke in the street was interested in fast algorithms for computing π(x), that would be a neat place!)
You'd seek out a mathematician, or visit a university library and ask for the maths librarian. If you didn't know about those resources, you'd go to your public library, and hopefully a librarian would point you in the right direction. All of these search algorithms still work today. :)
As someone who had to write letters for information or ask experts over the phone in the 70s, 80s, and part of the 90s (BBSs in the late 80s to 90s for me), you'd have to have good luck finding the person with the bit of specialized knowledge you sought, and hope they had it. A nostalgic note: Our sixth grade teacher made us pick four big companies and write letters to them asking for information about them and their products. I remember being ecstatic getting letters, pamphlets and even items from them. Toothpaste from Colgate. The pamphlets were so much more informative than the marketing material today. They were pitched to a smarter audience possibly purchasing agents, etc. hTe fastest response was almost three weeks. The rest came a month and later.
I was just a fledgling in the late days of the BBSs, so I didn't spend too much time there!
Fair points about the trouble of finding the right expert. I also wasn't on any of the math-related Usenet groups back in the day (I was more of a comp.lang.* lurker), but I wonder if there was a good mingling of experts and novices in those groups. These days, you can (e.g.) visit /r/math or /r/mathematics on Reddit, and you'll occasionally see interesting novice questions being picked up by PhDs across various math fields -- sometimes with surprisingly deep responses. It's rare that a novice question merits such attention, but the fact that it can can happen -- that such a forum exists -- is delightful.
You've also reminded me of something, vaguely -- one of the major US universities used to have a phone number that you could call and ask them about nearly anything. They would research the question and get back to you with an answer if they could. I wish I could remember which university it was, maybe the number still exists?
