Smarandache prime-digital sequence: Difference between revisions
Smarandache prime-digital sequence (view source)
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Largest Smarandache prime under 10000000: 7777753 (Smarandache prime 1903)
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">spds: 2..∞ | select.first:100 'x ->
and? -> prime? x
-> every? digits x => prime?
print "First 25 SPDS primes:"
print first.n: 25 spds
print ""
print ["100th SPDS prime:" last spds]</syntaxhighlight>
{{out}}
<pre>First 25 SPDS primes:
2 3 5 7 23 37 53 73 223 227 233 257 277 337 353 373 523 557 577 727 733 757 773 2237 2273
100th SPDS prime: 33223</pre>
=={{header|AWK}}==
Line 521 ⟶ 539:
Ten thousandth SPDS prime: 273,322,727
Largest SPDS prime less than 1,000,000,000: 777,777,773
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
Uses the [[Extensible_prime_generator#Delphi|Delphi Prime-Generator Object]]
<syntaxhighlight lang="Delphi">
procedure ShowSmarandachePrimes(Memo: TMemo);
{Show primes where all digits are also prime}
var Sieve: TPrimeSieve;
var I,J,P,Count: integer;
var S: string;
function AllDigitsPrime(N: integer): boolean;
{Test all digits on N to see if they are prime}
var I,Count: integer;
var IA: TIntegerDynArray;
begin
Result:=False;
GetDigits(N,IA);
for I:=0 to High(IA) do
if not Sieve.Flags[IA[I]] then exit;
Result:=True;
end;
begin
Sieve:=TPrimeSieve.Create;
try
{Build 1 million primes}
Sieve.Intialize(1000000);
Count:=0;
{Test if all digits of the number are prime}
for I:=0 to Sieve.PrimeCount-1 do
begin
P:=Sieve.Primes[I];
if AllDigitsPrime(P) then
begin
Inc(Count);
if Count<=25 then Memo.Lines.Add(IntToStr(Count)+' - '+IntToStr(P));
if Count=100 then
begin
Memo.Lines.Add('100th = '+IntToStr(P));
break;
end;
end;
end;
finally Sieve.Free; end;
end;
</syntaxhighlight>
{{out}}
<pre>
1 - 2
2 - 3
3 - 5
4 - 7
5 - 23
6 - 37
7 - 53
8 - 73
9 - 223
10 - 227
11 - 233
12 - 257
13 - 277
14 - 337
15 - 353
16 - 373
17 - 523
18 - 557
19 - 577
20 - 727
21 - 733
22 - 757
23 - 773
24 - 2237
25 - 2273
100th = 33223
Elapsed Time: 150.037 ms.
</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
n = 2
repeat
if isprim n = 1
h = n
while h > 0
d = h mod 10
if d < 2 or d = 4 or d = 6 or d > 7
break 1
.
h = h div 10
.
if h = 0
cnt += 1
if cnt <= 25
write n & " "
.
.
.
until cnt = 100
n += 1
.
print ""
print n
</syntaxhighlight>
{{out}}
<pre>
2 3 5 7 23 37 53 73 223 227 233 257 277 337 353 373 523 557 577 727 733 757 773 2237 2273
33223
</pre>
Line 826 ⟶ 971:
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Smarandache_prime-digital_sequence}}
'''Solution'''
[[File:Fōrmulæ - Smarandache prime-digital sequence 01.png]]
'''Case 1. Show the first 25 SPDS primes'''
[[File:Fōrmulæ - Smarandache prime-digital sequence 02.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 03.png]]
'''Case 2. Show the hundredth SPDS prime'''
[[File:Fōrmulæ - Smarandache prime-digital sequence 04.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 05.png]]
'''Additional cases. Show the 1000-th, 10,000-th and 100,000th SPDS primes'''
[[File:Fōrmulæ - Smarandache prime-digital sequence 06.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 07.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 08.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 09.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 10.png]]
[[File:Fōrmulæ - Smarandache prime-digital sequence 11.png]]
=={{header|Go}}==
Line 1,875 ⟶ 2,046:
</pre>
=={{header|RPL}}==
Brute force being not an option for the slow machines that can run RPL, optimisation is based on a prime-digital number generator returning possibly prime numbers, e.g. not ending by 2 or 5.
<code>PRIM?</code> is defined at [[Primality by trial division#RPL|Primality by trial division]].
{| class="wikitable"
! RPL code
! Comment
|-
|
≪ { "2" "3" "5" "7" } DUP SIZE → digits base
≪ DUP SIZE 1 CF 2 SF
'''DO'''
'''IF''' DUP NOT '''THEN''' digits 1 GET ROT + SWAP 1 CF
'''ELSE'''
DUP2 DUP SUB digits SWAP POS
'''IF''' 2 FS?C '''THEN''' 2 == 4 ≪ 1 SF 2 ≫ IFTE
'''ELSE IF''' DUP base == '''THEN'''
SIGN 1 SF '''ELSE''' 1 + 1 CF '''END'''
'''END'''
digits SWAP GET REPL
LASTARG ROT DROP2 1 - '''END'''
'''UNTIL''' 1 FC? '''END''' DROP
≫ ≫ ‘<span style="color:blue">'''NSPDP'''</span>’ STO
|
<span style="color:blue">'''NSPDP'''</span> ''( "PDnumber" → "nextPDnumber" )''
rank = units position, carry = 0, 1st pass = true
Loop
If rank = 0 then add a new digit rank
Else
digit = ord[rank]
If first pass then next digit = 3 or 7
Else if digit is the last of the series
Then next digit = 1 otherwise = ++digit
Replace digit with next_digit
Rank--
Until no carry
return number as a string
|}
≪ { 2 3 5 } 7
'''WHILE''' OVER SIZE 100 < '''REPEAT'''
'''IF''' DUP <span style="color:blue">'''PRIM?'''</span> '''THEN''' SWAP OVER + SWAP '''END'''
STR→ <span style="color:blue">'''NSPDP'''</span> STR→ '''END''' DROP ≫ EVAL
DUP 1 25 SUB
SWAP 100 GET
{{out}}
<pre>
2: { 2 3 5 7 23 37 53 73 223 227 233 257 277 337 353 373 523 557 577 727 733 757 773 2237 2273 }
1: 33223
</pre>
task needs 3 min 45 s to run on a HP-48G.
=={{header|Rust}}==
<syntaxhighlight lang="rust">fn is_prime(n: u32) -> bool {
Line 2,083 ⟶ 2,304:
{{libheader|Wren-math}}
Simple brute-force approach.
<syntaxhighlight lang="
var limit = 1000
| |||