Quadrat special primes: Difference between revisions

Content added Content deleted
(→‎{{header|Phix}}: added cubic code)
(→‎{{header|Ring}}: cleaned up columns, added additional degrees)
Line 366: Line 366:


=={{header|Ring}}==
=={{header|Ring}}==
<lang ring>
<lang ring>load "stdlib.ring"
load "stdlib.ring"
/* Searching for the smallest prime gaps under a limit,
such that the difference of successive terms (gaps)
is of the smallest degree. */


see "working..." + nl
? "working..."


desc = split("na quadratic cubic quartic quintic sextic septic octic nonic decic"," ")
Primes = []
limits = [1, 16000, 15000, 30000, 50000, 50000, 50000, 75000, 300000, 500000]
limit1 = 50
for deg = 2 to len(desc)
oldPrime = 1
add(Primes,2)


Primes = []
for n = 1 to limit1
limit = limits[deg]
nextPrime = oldPrime + pow(n,2)
oldPrime = 2
if isprime(nextPrime)
n = 1
add(Primes, 2)
add(Primes,nextPrime)
oldPrime = nextPrime
for n = 1 to sqrt(limit)
nextPrime = oldPrime + pow(n, deg)
else
nextPrime = nextPrime - oldPrime
if isprime(nextPrime)
ok
n = 1
if nextPrime < limit add(Primes, nextPrime) ok
oldPrime = nextPrime
else
nextPrime = nextPrime - oldPrime
ok
if nextPrime > limit exit ok
next
? nl + desc[deg] + ":" + nl + " prime1 prime2 Gap Rt"
for n = 1 to Len(Primes) - 1
diff = Primes[n + 1] - Primes[n]
? sf(Primes[n], 7) + " " + sf(Primes[n+1], 7) + " " + sf(diff, 6) + " " + sf(floor(0.49 + pow(diff, 1 / deg)), 4)
next
? "Found " + Len(Primes) + " primes under " + limit + " for " + desc[deg] + " gaps."
next
next
? nl + "done..."


# a very plain string formatter, intended to even up columnar outputs
see "prime1 prime2 Gap" + nl
def sf x, y
for n = 1 to Len(Primes)-1
diff = Primes[n+1] - Primes[n]
s = string(x) l = len(s)
if l > y y = l ok
see ""+ Primes[n] + " " + Primes[n+1] + " " + diff + nl
return substr(" ", 11 - y + l) + s</lang>
next
{{out}}
<pre style="height:20em">working...


quadratic:
see "Found " + Len(Primes) + " of the smallest primes < 16,000 such that the difference of successive terma are the smallest quadrat numbers" + nl
prime1 prime2 Gap Rt
2 3 1 1
3 7 4 2
7 11 4 2
11 47 36 6
47 83 36 6
83 227 144 12
227 263 36 6
263 587 324 18
587 911 324 18
911 947 36 6
947 983 36 6
983 1019 36 6
1019 1163 144 12
1163 1307 144 12
1307 1451 144 12
1451 1487 36 6
1487 1523 36 6
1523 1559 36 6
1559 2459 900 30
2459 3359 900 30
3359 4259 900 30
4259 4583 324 18
4583 5483 900 30
5483 5519 36 6
5519 5843 324 18
5843 5879 36 6
5879 6203 324 18
6203 6779 576 24
6779 7103 324 18
7103 7247 144 12
7247 7283 36 6
7283 7607 324 18
7607 7643 36 6
7643 8219 576 24
8219 8363 144 12
8363 10667 2304 48
10667 11243 576 24
11243 11279 36 6
11279 11423 144 12
11423 12323 900 30
12323 12647 324 18
12647 12791 144 12
12791 13367 576 24
13367 13691 324 18
13691 14591 900 30
14591 14627 36 6
14627 14771 144 12
14771 15671 900 30
Found 49 primes under 16000 for quadratic gaps.


cubic:
see nl + "done..." + nl
prime1 prime2 Gap Rt
</lang>
2 3 1 1
{{out}}
3 11 8 2
<pre>
11 19 8 2
working...
19 83 64 4
prime1 prime2 Gap
2 3 1
83 1811 1728 12
3 7 4
1811 2027 216 6
7 11 4
2027 2243 216 6
11 47 36
2243 2251 8 2
47 83 36
2251 2467 216 6
83 227 144
2467 2531 64 4
227 263 36
2531 2539 8 2
263 587 324
2539 3539 1000 10
587 911 324
3539 3547 8 2
911 947 36
3547 4547 1000 10
947 983 36
4547 5059 512 8
983 1019 36
5059 10891 5832 18
1019 1163 144
10891 12619 1728 12
1163 1307 144
12619 13619 1000 10
1307 1451 144
13619 13627 8 2
1451 1487 36
13627 13691 64 4
1487 1523 36
13691 13907 216 6
1523 1559 36
13907 14419 512 8
Found 23 primes under 15000 for cubic gaps.
1559 2459 900

2459 3359 900
quartic:
3359 4259 900
4259 4583 324
prime1 prime2 Gap Rt
4583 5483 900
2 3 1 1
5483 5519 36
3 19 16 2
Found 3 primes under 30000 for quartic gaps.
5519 5843 324

5843 5879 36
quintic:
5879 6203 324
6203 6779 576
prime1 prime2 Gap Rt
6779 7103 324
2 3 1 1
7103 7247 144
3 32771 32768 8
7247 7283 36
32771 32803 32 2
7283 7607 324
32803 33827 1024 4
7607 7643 36
33827 41603 7776 6
Found 6 primes under 50000 for quintic gaps.
7643 8219 576

8219 8363 144
sextic:
8363 10667 2304
10667 11243 576
prime1 prime2 Gap Rt
11243 11279 36
2 3 1 1
11279 11423 144
3 67 64 2
11423 12323 900
67 131 64 2
Found 4 primes under 50000 for sextic gaps.
12323 12647 324

12647 12791 144
septic:
12791 13367 576
13367 13691 324
prime1 prime2 Gap Rt
13691 14591 900
2 3 1 1
14591 14627 36
3 131 128 2
Found 3 primes under 50000 for septic gaps.
14627 14771 144

14771 15671 900
octic:
Found 49 of the smallest primes < 16,000 such that the difference of successive terma are the smallest quadrat numbers
prime1 prime2 Gap Rt
done...
2 3 1 1
</pre>
3 65539 65536 4
Found 3 primes under 75000 for octic gaps.

nonic:
prime1 prime2 Gap Rt
2 3 1 1
3 262147 262144 4
Found 3 primes under 300000 for nonic gaps.

decic:
prime1 prime2 Gap Rt
2 3 1 1
Found 2 primes under 500000 for decic gaps.

done...</pre>


=={{header|Wren}}==
=={{header|Wren}}==
Retrieved from "https://rosettacode.org/wiki/Quadrat_special_primes"