Primes which contain only one odd digit: Difference between revisions
Primes which contain only one odd digit (view source)
Revision as of 08:20, 8 September 2021
, 2 years ago→{{header|jq}}
m (Peak moved page Primes which contain only one odd number to Primes which contain only one odd digit: clarity) |
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Count of matches below 10E6:
2560</pre>
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
As noted in the [[#Julia|Julia entry]], if only one digit of a prime is odd, then that digit is in the ones place. The first solution presented here uses this observation to generate plausible candidates. The second solution is more brutish and slower but simpler.
See e.g. [[Erd%C5%91s-primes#jq]] for a suitable implementation of `is_prime`.
===Fast solution===
<lang jq>### Preliminaries
def count(s): reduce s as $x (null; .+1);
def emit_until(cond; stream):
label $out | stream | if cond then break $out else . end;
# Output: an unbounded stream
def primes_with_exactly_one_odd_digit:
# Output: a stream of candidate strings, in ascending numerical order
def candidates:
# input is $width
def evens:
. as $width
| if $width == 0 then ""
else ("0","2","4","6","8") as $i
| ((.-1)|evens) as $j
| "\($i)\($j)"
end;
("2","4","6","8") as $leading
| evens as $even
| ("1","3","5","7","9") as $odd
| "\($leading)\($even)\($odd)";
(3,5,7),
(range(0; infinite)
| candidates | tonumber
| select(is_prime)) ;
### The Task
emit_until(. > 1000; primes_with_exactly_one_odd_digit),
"\nThe number of primes less than 1000000 with exactly one odd digits is \(count(emit_until(. > 1000000; primes_with_exactly_one_odd_digit)))."/lang>
{{out}}
<pre>
3
5
7
23
29
41
43
47
61
67
83
89
223
227
229
241
263
269
281
283
401
409
421
443
449
461
463
467
487
601
607
641
643
647
661
683
809
821
823
827
829
863
881
883
887
The number of primes less than 1000000 with exactly one odd digits is 2560.
</pre>
=== A simpler but slower solution ===
<lang jq># Input is assumed to be prime.
# So we only need check the other digits are all even.
def prime_has_exactly_one_odd_digit:
if . == 2 then false
# The codepoints for the odd digits are also odd: [49,51,53,55,57]
else all(tostring | explode[:-1][]; . % 2 == 0)
end;
def primes_with_exactly_one_odd_digit_crudely:
# It is much faster to check for primality afterwards.
range(3; infinite; 2)
| select(prime_has_exactly_one_odd_digit and is_prime);</lang>
</lang>
=={{header|Julia}}==
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