Do you think I could just leave this part blank and it'd be okay? We're just going to replace the whole thing with a header image anyway, right?
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44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999, are primes.
But can can you do it faster than google?
One bot to rule them all, one bot to find them. One bot to bring them all... and with this cliché blind them.
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string primes = ""
for (int i = 1; i <= 50000; i++)
{
bool is_prime = true;
for (int z = 1; z < i; z++)
{
if (i % z == 0 & z != 1 && z != i)
{
is_prime = false;
}
}
if (is_prime)
{
primes += i.toString() + ", ";
}
}
primes += "are primes.";
MsgBox(primes);
F
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for (let i = 2; i <= 50000; i++) {
let prime = true;
for (let j = 2; j * j <= i; j++) {
if (i % j == 0) {
prime = false;
break;
}
}
if (prime) document.write(i + ", ");
}
document.write("are primes.");
Slightly more efficient
(You only need to check numbers up to the square root of the number, as factors come in pairs, one below the square root and one above)
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string primes = ""
for (int i = 1; i <= 50000; i++)
{
bool is_prime = true;for (int z = 1; z < i; z++)
{
if (i % z == 0 & z != 1 && z != i)
{
is_prime = false;
}
}
if (is_prime)
{
primes += i.toString() + ", ";
}
}primes += "are primes.";
MsgBox(primes);
And how long did it took you?
I'm surprised this actually spurned conversation
are you guys limiting your loops to the square root of the number you're testing for primality? After all, one only needs find one of a factor pairing... and the factor pairs straddle the square root of the number....
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for (let i = 2; i <= 50000; i++)
if(isPrime(i)) document.write(i + ", ");
document.write("are primes.");
ya all n00bs
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Andymakeer wrote:string primes = ""
for (int i = 1; i <= 50000; i++)
{
bool is_prime = true;for (int z = 1; z < i; z++)
{
if (i % z == 0 & z != 1 && z != i)
{
is_prime = false;
}
}
if (is_prime)
{
primes += i.toString() + ", ";
}
}primes += "are primes.";
MsgBox(primes);And how long did it took you?
idk lol just posted not actually run it on C#
for (let i = 2; i <= 50000; i++) {
let prime = true;
for (let j = 2; j * j <= i; j++) {
if (i % j == 0) {
prime = false;
break;
}
}
if (prime) document.write(i + ", ");
}
document.write("are primes.");
ewwww console application
F
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LukeM wrote:for (let i = 2; i <= 50000; i++) {
let prime = true;
for (let j = 2; j * j <= i; j++) {
if (i % j == 0) {
prime = false;
break;
}
}
if (prime) document.write(i + ", ");
}
document.write("are primes.");ewwww console application
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it'd cool to have a Hackaton topic at forums games...
F
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Stack Overflow would lynch you all.
1. Why on Earth are you checking if even numbers are prime?
2. If it’s not divisible by 3 then it’s certainly not divisible by 9. The set of numbers used for the modulus should itself be prime.
One bot to rule them all, one bot to find them. One bot to bring them all... and with this cliché blind them.
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Stack Overflow would lynch you all.
1. Why on Earth are you checking if even numbers are prime?
2. If it’s not divisible by 3 then it’s certainly not divisible by 9. The set of numbers used for the modulus should itself be prime.
1. It makes almost no difference checking even numbers in my example, the first check is % 2 and after that it breaks so doesn't check anything else. At low primes this may seem like it matters, but once you get larger this time is nothing compared to the time needed to check less trivial numbers.
2. Fine... Edit: Although in some cases storing all the primes below the current number isn't plausible, e.g. once you get to searching for very large primes, or sometimes it might just be slower, e.g. when finding the first prime after 1000000
let primes = [ ];
for (let i = 2; i <= 50000; i++) {
let prime = true;
for (let j = 0, p; (p = primes[j]) && p * p <= i; j++) {
if (i % p == 0) {
prime = false;
break;
}
}
if (prime) primes.push(i);
}
document.write([...primes, "are primes."].join(", "));
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I know an easier way… Just write all 50,000 numbers, then remove all numbers dividable with 2, 3, 5, 7, 11, 13, 17, 19, 23... I mean, just divide it with another prime numbers
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We can compare algorithms that generate primes of up to 50,000 by counting the number of modulo operations they require. The most efficient algorithm is the one that performs the fewest.
(Don’t be a **** and pull the primes from a webpage or use division instead of modulus.)
@LukeM:
“Trivial” is subjective and depends on your use-case. A number of “trivial” incremental improvements can sum to a decent bump in performance. In any case it defies logic to perform a single % on an even number.
One bot to rule them all, one bot to find them. One bot to bring them all... and with this cliché blind them.
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“Trivial” is subjective and depends on your use-case. A number of “trivial” incremental improvements can sum to a decent bump in performance. In any case it defies logic to perform a single % on an even number.
In this case you can continue to optimise infinitely, why not also hardcode the skipping of multiples of 3 too? Or 5?
All these things will speed up the code slightly, the difference just tends to 0 as you go further.
Number of modulo operations when hardcoding the skipping of certain multiples:
Check up to Hardcode none Hardcode up to 2 Hardcode up to 3 Hardcode up to 5 Hardcode up to 7
10 8 1 12.5% 0 00.0% 0 00.0% 0 00.0%
100 181 84 46.4% 38 21.0% 13 07.2% 0 00.0%
1000 2801 1804 64.4% 1308 46.7% 983 35.1% 730 26.1%
10000 43753 33756 77.2% 28760 65.7% 25435 58.1% 22782 52.1%
100000 744436 644439 86.6% 594443 79.9% 561118 75.4% 534465 71.8%
1000000 13927402 12927405 92.8% 12427409 89.2% 12094084 86.8% 11827431 84.9%
10000000 286144938 276144941 96.5% 271144945 94.8% 267811620 93.6% 265144967 92.7%
100000000 6320928470 6220928473 98.4% 6170928477 97.6% 6137595152 97.1% 6110928499 96.7%
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On my PC, if my algorithm:
Uses i += 2, and;
Therefore never needs to do (i % 2),
For i = 50,000 it does 84.06% of the modulo operations of the unoptimised algorithm, and takes 8.21ms vs 11.25ms. --> 3ms saved.
For i = 100,000,000 it does 95.06% of the operations, and takes 65.47s vs 76.57s. --> 11s saved.
In the context of this thread, of checking a relatively small set of numbers with a very simple algorithm, those savings aren't negligible.
And for finding Mersenne primes, optimisation like that is probably critical. Imagine if the guy running a supercomputer said, "Yeah it's only 1% faster, don't bother." That difference could mean days of time and thousands of $$$ saved.
One bot to rule them all, one bot to find them. One bot to bring them all... and with this cliché blind them.
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But why stop there? If you go with 2 hops you could as easily go with 6 hops.
bool is_prime(int x) {
if (x <= 1) return false;
if (x <= 3) return true;if (x % 2 == 0 || x % 3 == 0) return false;
int i = 5;
int sq_root = (int) sqrt(x);while (i <= sq_root) {
if (x % i == 0 || x % (i + 2) == 0)
return false;
i += 6;
}return true;
}
Everybody edits, but some edit more than others
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On my PC, if my algorithm:
Uses i += 2, and;
Therefore never needs to do (i % 2),
For i = 50,000 it does 84.06% of the modulo operations of the unoptimised algorithm, and takes 8.21ms vs 11.25ms. --> 3ms saved.
For i = 100,000,000 it does 95.06% of the operations, and takes 65.47s vs 76.57s. --> 11s saved.
In the context of this thread, of checking a relatively small set of numbers with a very simple algorithm, those savings aren't negligible.
And for finding Mersenne primes, optimisation like that is probably critical. Imagine if the guy running a supercomputer said, "Yeah it's only 1% faster, don't bother." That difference could mean days of time and thousands of $$$ saved.
My algorithm was pretty much the same, just I did all of the modulos but kept track of which ones would have been used in each of the optimisations. I guess tomorrow I'll go back and check through what I did to see if I went wrong somewhere...
Edit: I've gone through and checked my algorithm against the += 2 algorithm its attempting to model and it seems to be consistent... I guess ill paste it here so we can compare maybe:
And I guess yes, in this case it does make a noticeable difference in the time taken to execute, but I would argue that being 10% faster doesn't really matter in this case because it only saves seconds, and as the numbers you are calculating get larger and larger the time taken to calculate the primes scales much faster than the time saved, meaning that before the saved time is more than a minute or two the total time is so large that that doesn't matter anymore.
And for numbers the size of mersenne primes something like this would make almost no difference (it must take minutes to check large mersenne primes now, so a few ms to modulo 2 wouldn't matter at all (ignoring the fact that you don't need to modulo 2 as 2^n - 1 is always odd)
Sure some micro optimisations would matter, something that would save a constant proportion of the time would be great (even 1% as you say), but something like this where the time saved decays exponentially (citation needed) doesn't really make a difference.
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random short story
so my uni took a few teams to a programming competition a while back. It was great. One of the problems asked about finding all the circular primes from 0 to 50,000.
They figured out some fancy methods with logs or something that skipped the whole "oh should we convert it to a string to loop it" issue.
They even remembered to stop the loop at the sqrt of the number when checking for primality...
Then they got creative and decided that they should start at 1 and increment by two for each modulo check
They tried tons of different data parameters to debug why their program submission wasn't working
afterwards I reminded them about the number two
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https://codea.io/talk/discussion/9216/a … am-i-wrote
This is how I have done that, but in present I found a better algorithm.
I'm a nub
for(var i = 1; i < 50,000; i++) {
if(Math.sqrt(i) = Math.round(Math.sqrt(i))) {
console.log(i)
}
}
Haven't tested it out but it's probably a cheap way to do it...
EDIT: just realised that the square root of 8 isn't a whole number either... 2x4 2^3...
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I'm a nub
for(var i = 1; i < 50,000; i++) { if(Math.sqrt(i) = Math.round(Math.sqrt(i))) { console.log(i) } }
Haven't tested it out but it's probably a cheap way to do it...
EDIT: just realised that the square root of 8 isn't a whole number either... 2x4 2^3...
That would only check for square numbers, not all composite numbers. I'm pretty sure there isn't a better (simple) way to do it than the way we all did it.
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These primes only go up to 49,999.
obvious sarcasm
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I'm surprised this actually spurned conversation
are you guys limiting your loops to the square root of the number you're testing for primality? After all, one only needs find one of a factor pairing... and the factor pairs straddle the square root of the number....
But why? You could create an array, where all primes are kept, and then only going trough the primes, and only through the primes that are below the square root of the number.
That is, if we would check 100 for primality, we would only go trough 2, 3, 5 and 7 (and obviously stop at 2).
hummerz5 wrote:I'm surprised this actually spurned conversation
are you guys limiting your loops to the square root of the number you're testing for primality? After all, one only needs find one of a factor pairing... and the factor pairs straddle the square root of the number....
But why? You could create an array, where all primes are kept, and then only going trough the primes, and only through the primes that are below the square root of the number.
That is, if we would check 100 for primality, we would only go trough 2, 3, 5 and 7 (and obviously stop at 2).
Thats what Hummerz5 was saying wasn't it? (That you only check divisors up to the square root of the number)
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[ Started around 1714098573.198 - Generated in 0.213 seconds, 11 queries executed - Memory usage: 1.89 MiB (Peak: 2.24 MiB) ]