Erdős-primes: Difference between revisions
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The 7875th Erdos prime is 999721.
</pre>
=={{header|ABC}}==
<syntaxhighlight lang="abc">HOW TO REPORT prime n:
SELECT:
n < 2: FAIL
n mod 2 = 0: REPORT n=2
ELSE: REPORT NO d IN {2..floor (root n)} HAS n mod d = 0
HOW TO REPORT erdos p:
IF NOT prime p: FAIL
PUT 1, 1 IN k, k.fac
WHILE k.fac < p:
IF prime (p - k.fac): FAIL
PUT k+1 IN k
PUT k.fac*k IN k.fac
SUCCEED
PUT 0 IN nprimes
FOR n IN {1..2499}:
IF erdos n:
WRITE n>>6
PUT nprimes+1 IN nprimes
IF nprimes mod 10 = 0: WRITE/
WRITE /
WRITE "There are `nprimes` Erdos primes < 2500."/
PUT 2499 IN n
WHILE nprimes < 7875:
PUT n+2 IN n
IF erdos n: PUT nprimes + 1 IN nprimes
WRITE "The `nprimes`th Erdos prime is `n`."/</syntaxhighlight>
{{out}}
<pre> 2 101 211 367 409 419 461 557 673 709
769 937 967 1009 1201 1259 1709 1831 1889 2141
2221 2309 2351 2411 2437
There are 25 Erdos primes < 2500.
The 7875th Erdos prime is 999721.</pre>
=={{header|Action!}}==
Line 177 ⟶ 216:
999721 is Erdos prime 7875
</pre>
=={{header|APL}}==
<syntaxhighlight lang="apl">erdos_primes←{
prime ← {(⍵≥2) ∧ 0∧.≠(1↓⍳⌊⍵*÷2)|⍵}
erdos ← {(prime ⍵) ∧ ∧/~prime¨ ⍵-!⍳⌊(!⍣¯1)⍵}
e2500 ← (erdos¨e)/e←⍳2500
⎕←e2500
⎕←'There are ',(⍕⍴e2500),' Erdős numbers ≤ 2500'
}</syntaxhighlight>
{{out}}
<pre>2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437
There are 25 Erdős numbers ≤ 2500</pre>
=={{header|Arturo}}==
Line 702 ⟶ 753:
</pre>
=={{header|EasyLang}}==
{{trans|Action!}}
<syntaxhighlight>
fastfunc isprim num .
if num < 2
return 0
.
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
func iserdosprim p .
if isprim p = 0
return 0
.
k = 1
f = 1
while f < p
if isprim (p - f) = 1
return 0
.
k += 1
f *= k
.
return 1
.
for p = 2 to 2499
if iserdosprim p = 1
write p & " "
.
.
</syntaxhighlight>
{{out}}
<pre>
2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437
</pre>
=={{header|F_Sharp|F#}}==
Line 718 ⟶ 811:
7875th Erdos prime is 999721
</pre>
=={{header|Factor}}==
{{works with|Factor|0.99 2021-02-05}}
Line 1,132 ⟶ 1,226:
25
{7875, 999721}</pre>
=={{header|Miranda}}==
<syntaxhighlight lang="miranda">main :: [sys_message]
main = [Stdout (lay (map show erdos2500)),
Stdout ("There are " ++ show (#erdos2500) ++ " Erdos numbers <2500\n")]
where erdos2500 = filter erdos [1..2499]
erdos :: num->bool
erdos p = prime p & ~or [prime (p-k) | k <- takewhile (<p) (scan (*) 1 [2..])]
prime :: num->bool
prime n = n=2 \/ n=3, if n<=4
prime n = False, if n mod 2=0
prime n = and [n mod d ~= 0 | d <- [2..entier (sqrt n)]]</syntaxhighlight>
{{out}}
<pre>2
101
211
367
409
419
461
557
673
709
769
937
967
1009
1201
1259
1709
1831
1889
2141
2221
2309
2351
2411
2437
There are 25 Erdos numbers <2500</pre>
=={{header|Nim}}==
Line 1,674 ⟶ 1,809:
</pre>
=={{header|SETL}}==
<syntaxhighlight lang="setl">program erdos_primes;
loop for e in [1..2499] | erdos e do
nprint(lpad(str e, 6));
if (n +:= 1) mod 10=0 then print; end if;
end loop;
print;
print("There are " + str n + " Erdos numbers < 2500");
e := 2499;
loop while n < 7875 do
loop until erdos e do
e +:= 2;
end loop;
n +:= 1;
end loop;
print("The " + str n + "th Erdos number is " + str e);
op erdos(p);
return prime p and not exists k in faclist p | prime (p-k);
end erdos;
op faclist(n);
f := 1;
return [[i+:=1, f*:=i](2) : until n<f](..i-1);
end op;
op prime(n);
if n<=4 then
return n in [2,3];
end if;
return odd n and not exists d in [3, 5..floor (sqrt n)] | n mod d=0;
end op;
end program;</syntaxhighlight>
{{out}}
<pre> 2 101 211 367 409 419 461 557 673 709
769 937 967 1009 1201 1259 1709 1831 1889 2141
2221 2309 2351 2411 2437
There are 25 Erdos numbers < 2500
The 7875th Erdos number is 999721</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func is_erdos_prime(p) {
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