Primes: n*2^m+1: Difference between revisions
Add PARI/GP implementation
(Add PARI/GP implementation) |
|||
| (20 intermediate revisions by 10 users not shown) | |||
Line 1:
{{task}}
;Task
* Find and display the first 45 ('''n''') primes of the form '''n × 2<sup>m</sup> + 1''' where '''m''' is the smallest valid non-negative integer.
Line 9:
;Stretch harder
* Find and display the first 400 ('''n''') primes of the form '''n × 2<sup>m</sup> + 1''' where '''m''' is the smallest valid non-negative integer. ''Specifically term 383.''
Line 17:
=={{header|ALGOL 68}}==
{{works with|ALGOL 68G|
{{libheader|ALGOL 68-primes}}
The values of the primes are interesting - most will fit in 64 bits (those up to 45 will fit in 16 bits) but there are a small number that have hundreds or thousands of digits. <br>
<b>NB</b> the primes.incl.a68 source is available on a page in Rosetta Code - see the <b>library</b> above.
<syntaxhighlight lang="algol68">
Line 450:
400 0: 401
</pre>
=={{header|ALGOL W}}==
Although most of the primes up to 500 will fit in 32 bits, obviously 383 won't, having over 6000 digits, so this doesn;t attempt to show more than the first 45. NB: 47 is the first prime that won't fit in 32 bits.
<syntaxhighlight lang="algolw">
begin % find primes of the form 1+n*2^m where m is the lowest integer >= 0 %
% such that 1+n*2^m is prime %
integer MAX_M, MAX_PRIME;
MAX_M := 22;
MAX_PRIME := 10000;
begin
logical array prime ( 1 :: MAX_PRIME );
% sieve the primes to MAX_PRIME %
prime( 1 ) := false; prime( 2 ) := true;
for i := 3 step 2 until MAX_PRIME do prime( i ) := true;
for i := 4 step 2 until MAX_PRIME do prime( i ) := false;
for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin
integer ii; ii := i + i;
if prime( i ) then for pr := i * i step ii until MAX_PRIME do prime( pr ) := false
end for_i ;
% find the n*2^m + 1 primes %
for n := 1 until 45 do begin
integer m, twoToM, p;
logical notFound;
m := 0;
twoToM := 1;
p := 0;
notFound := true;
while notFound and m <= MAX_M do begin
p := ( n * twoToM ) + 1;
notFound := not prime( p );
if notFound then begin
twoToM := twoToM + twoToM;
m := m + 1
end if_notFound
end while_notFound_and_m_le_MAX_M ;
if notFound
then writeon( i_w := 3, s_w := 0, "(", n, " not found)" )
else writeon( i_w := 3, s_w := 0, "(", n, " ", i_w := 1, m, ": ", i_w := 4, p, " )" );
if n rem 5 = 0 then write()
end for_n
end
end.
</syntaxhighlight>
{{out}}
<pre>
( 1 0: 2 )( 2 0: 3 )( 3 1: 7 )( 4 0: 5 )( 5 1: 11 )
( 6 0: 7 )( 7 2: 29 )( 8 1: 17 )( 9 1: 19 )( 10 0: 11 )
( 11 1: 23 )( 12 0: 13 )( 13 2: 53 )( 14 1: 29 )( 15 1: 31 )
( 16 0: 17 )( 17 3: 137 )( 18 0: 19 )( 19 6: 1217 )( 20 1: 41 )
( 21 1: 43 )( 22 0: 23 )( 23 1: 47 )( 24 2: 97 )( 25 2: 101 )
( 26 1: 53 )( 27 2: 109 )( 28 0: 29 )( 29 1: 59 )( 30 0: 31 )
( 31 8: 7937 )( 32 3: 257 )( 33 1: 67 )( 34 2: 137 )( 35 1: 71 )
( 36 0: 37 )( 37 2: 149 )( 38 5: 1217 )( 39 1: 79 )( 40 0: 41 )
( 41 1: 83 )( 42 0: 43 )( 43 2: 173 )( 44 1: 89 )( 45 2: 181 )
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">cnt: 0
n: 1
while [cnt < 45][
m: 0
while [true][
p: inc n * 2^m
if prime? p [
print ["n:" n "m:" m "p:" p]
inc 'cnt
break
]
inc 'm
]
inc 'n
]</syntaxhighlight>
{{out}}
<pre>n: 1 m: 0 p: 2
n: 2 m: 0 p: 3
n: 3 m: 1 p: 7
n: 4 m: 0 p: 5
n: 5 m: 1 p: 11
n: 6 m: 0 p: 7
n: 7 m: 2 p: 29
n: 8 m: 1 p: 17
n: 9 m: 1 p: 19
n: 10 m: 0 p: 11
n: 11 m: 1 p: 23
n: 12 m: 0 p: 13
n: 13 m: 2 p: 53
n: 14 m: 1 p: 29
n: 15 m: 1 p: 31
n: 16 m: 0 p: 17
n: 17 m: 3 p: 137
n: 18 m: 0 p: 19
n: 19 m: 6 p: 1217
n: 20 m: 1 p: 41
n: 21 m: 1 p: 43
n: 22 m: 0 p: 23
n: 23 m: 1 p: 47
n: 24 m: 2 p: 97
n: 25 m: 2 p: 101
n: 26 m: 1 p: 53
n: 27 m: 2 p: 109
n: 28 m: 0 p: 29
n: 29 m: 1 p: 59
n: 30 m: 0 p: 31
n: 31 m: 8 p: 7937
n: 32 m: 3 p: 257
n: 33 m: 1 p: 67
n: 34 m: 2 p: 137
n: 35 m: 1 p: 71
n: 36 m: 0 p: 37
n: 37 m: 2 p: 149
n: 38 m: 5 p: 1217
n: 39 m: 1 p: 79
n: 40 m: 0 p: 41
n: 41 m: 1 p: 83
n: 42 m: 0 p: 43
n: 43 m: 2 p: 173
n: 44 m: 1 p: 89
n: 45 m: 2 p: 181</pre>
=={{header|EasyLang}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang=easylang>
func isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
for n = 1 to 45
m = 0
repeat
p = n * (pow 2 m) + 1
until isprim p = 1
m += 1
.
print n & " " & m & " " & p
.
</syntaxhighlight>
=={{header|FreeBASIC}}==
Line 518 ⟶ 664:
(Most of the implementation here is about merging intermediate values and formatting for display. The calculation for m is <code>i.&1"1]1 p:1+(1+i.45) */ 2^i.9</code> -- for n in the range 1..45, try all m exponents in the range 0..8 and find the first m value for each n which corresponds to a prime.)
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq.'''
gojq supports unbounded-precision integer arithmetic but the following
algorithm for prime number detection is not up to the stretch tasks.
<syntaxhighlight lang=jq>
# Input should be an integer
# No sqrt!
def isPrime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
else 5
| until( . <= 0;
if .*. > $n then -1
elif ($n % . == 0) then 0
else . + 2
| if ($n % . == 0) then 0
else . + 4
end
end)
| . == -1
end;
# Emit [m, n*2**m+1] where m is smallest non-negative integer such that n * 2**m + 1 is prime
# WARNING: continues searching ad infinitum ...
def n2m1:
. as $n
| first(
foreach range(0; infinite) as $m (null;
if . == null then 1 else 2*. end;
(. * $n + 1)
| select(isPrime) | [$m, .] ) ) ;
# The task:
"[N,M,Prime]\n------------------",
( range(1;45) | [.] + n2m1 )
</syntaxhighlight>
'''Invocation''': jq -nrc -f n2m1.jq
{{output}}
<pre>
[1,0,2]
[2,0,3]
[3,1,7]
[4,0,5]
[5,1,11]
[6,0,7]
[7,2,29]
[8,1,17]
[9,1,19]
[10,0,11]
[11,1,23]
[12,0,13]
[13,2,53]
[14,1,29]
[15,1,31]
[16,0,17]
[17,3,137]
[18,0,19]
[19,6,1217]
[20,1,41]
[21,1,43]
[22,0,23]
[23,1,47]
[24,2,97]
[25,2,101]
[26,1,53]
[27,2,109]
[28,0,29]
[29,1,59]
[30,0,31]
[31,8,7937]
[32,3,257]
[33,1,67]
[34,2,137]
[35,1,71]
[36,0,37]
[37,2,149]
[38,5,1217]
[39,1,79]
[40,0,41]
[41,1,83]
[42,0,43]
[43,2,173]
[44,1,89]
[45,2,181]
[46,0,47]
</pre>
=={{header|Julia}}==
Line 941 ⟶ 1,178:
399 2 1597
400 0 401
</pre>
=={{header|Nim}}==
===Task===
<syntaxhighlight lang = "Nim">import std/strformat
func isPrime(n: Natural): bool =
if n < 2: return false
if (n and 1) == 0: return n == 2
if n mod 3 == 0: return n == 3
var k = 5
var delta = 2
while k * k <= n:
if n mod k == 0: return false
inc k, delta
delta = 6 - delta
result = true
echo " n m prime"
for n in 1..45:
var m = 0
var term = n
while true:
if isPrime(term + 1):
echo &"{n:2} {m} {term + 1:5}"
break
inc m
term *= 2
</syntaxhighlight>
{{out}}
<pre style="height:12ex;overflow:scroll;>> n m prime
1 0 2
2 0 3
3 1 7
4 0 5
5 1 11
6 0 7
7 2 29
8 1 17
9 1 19
10 0 11
11 1 23
12 0 13
13 2 53
14 1 29
15 1 31
16 0 17
17 3 137
18 0 19
19 6 1217
20 1 41
21 1 43
22 0 23
23 1 47
24 2 97
25 2 101
26 1 53
27 2 109
28 0 29
29 1 59
30 0 31
31 8 7937
32 3 257
33 1 67
34 2 137
35 1 71
36 0 37
37 2 149
38 5 1217
39 1 79
40 0 41
41 1 83
42 0 43
43 2 173
44 1 89
45 2 181
</pre>
===Stretch tasks===
{{libheader|Nim-Integers}}
<syntaxhighlight lang = "Nim">import std/strformat
import integers
func compressed(str: string; size: int): string =
## Return a compressed value for long strings of digits.
if str.len <= 2 * size: str
else: &"{str[0..<size]}...{str[^size..^1]} ({str.len} digits)"
echo " n m prime"
for n in 1..400:
var m = 0
var term = newInteger(n)
while true:
if isPrime(term + 1):
echo &"{n:3} {m:4} {compressed($(term + 1), 10)}"
break
inc m
term *= 2
</syntaxhighlight>
{{out}}
<pre style="height:12ex;overflow:scroll;"> n m prime
1 0 2
2 0 3
3 1 7
4 0 5
5 1 11
6 0 7
7 2 29
8 1 17
9 1 19
10 0 11
11 1 23
12 0 13
13 2 53
14 1 29
15 1 31
16 0 17
17 3 137
18 0 19
19 6 1217
20 1 41
21 1 43
22 0 23
23 1 47
24 2 97
25 2 101
26 1 53
27 2 109
28 0 29
29 1 59
30 0 31
31 8 7937
32 3 257
33 1 67
34 2 137
35 1 71
36 0 37
37 2 149
38 5 1217
39 1 79
40 0 41
41 1 83
42 0 43
43 2 173
44 1 89
45 2 181
46 0 47
47 583 1487939695...6574002177 (178 digits)
48 1 97
49 2 197
50 1 101
51 1 103
52 0 53
53 1 107
54 1 109
55 4 881
56 1 113
57 2 229
58 0 59
59 5 1889
60 0 61
61 4 977
62 7 7937
63 1 127
64 2 257
65 1 131
66 0 67
67 2 269
68 1 137
69 1 139
70 0 71
71 3 569
72 0 73
73 2 293
74 1 149
75 1 151
76 4 1217
77 3 617
78 0 79
79 2 317
80 3 641
81 1 163
82 0 83
83 1 167
84 2 337
85 4 1361
86 1 173
87 2 349
88 0 89
89 1 179
90 1 181
91 8 23297
92 7 11777
93 2 373
94 582 1487939695...6574002177 (178 digits)
95 1 191
96 0 97
97 2 389
98 1 197
99 1 199
100 0 101
101 3 809
102 0 103
103 16 6750209
104 5 3329
105 1 211
106 0 107
107 3 857
108 0 109
109 6 6977
110 3 881
111 1 223
112 0 113
113 1 227
114 1 229
115 2 461
116 1 233
117 3 937
118 4 1889
119 1 239
120 1 241
121 8 30977
122 3 977
123 6 7873
124 6 7937
125 1 251
126 0 127
127 2 509
128 1 257
129 3 1033
130 0 131
131 1 263
132 4 2113
133 4 2129
134 1 269
135 1 271
136 0 137
137 3 1097
138 0 139
139 2 557
140 1 281
141 1 283
142 2 569
143 53 1288029493427961857
144 2 577
145 6 9281
146 1 293
147 8 37633
148 0 149
149 3 1193
150 0 151
151 4 2417
152 3 1217
153 1 307
154 2 617
155 1 311
156 0 157
157 8 40193
158 1 317
159 6 10177
160 2 641
161 3 1289
162 0 163
163 2 653
164 9 83969
165 1 331
166 0 167
167 7 21377
168 1 337
169 2 677
170 3 1361
171 8 43777
172 0 173
173 1 347
174 1 349
175 2 701
176 1 353
177 2 709
178 0 179
179 1 359
180 0 181
181 4 2897
182 7 23297
183 1 367
184 6 11777
185 3 1481
186 1 373
187 6 11969
188 581 1487939695...6574002177 (178 digits)
189 1 379
190 0 191
191 1 383
192 0 193
193 2 773
194 1 389
195 4 3121
196 0 197
197 15 6455297
198 0 199
199 2 797
200 1 401
201 3 1609
202 2 809
203 13 1662977
204 1 409
205 2 821
206 15 6750209
207 2 829
208 4 3329
209 1 419
210 0 211
211 20 221249537
212 3 1697
213 2 853
214 2 857
215 1 431
216 1 433
217 66 1601177385...9890802689 (23 digits)
218 5 6977
219 1 439
220 2 881
221 1 443
222 0 223
223 8 57089
224 1 449
225 3 1801
226 0 227
227 11 464897
228 0 229
229 6 14657
230 1 461
231 1 463
232 0 233
233 1 467
234 2 937
235 2 941
236 3 1889
237 4 3793
238 0 239
239 1 479
240 0 241
241 36 16561393893377
242 7 30977
243 1 487
244 2 977
245 1 491
246 5 7873
247 6 15809
248 5 7937
249 1 499
250 0 251
251 1 503
252 2 1009
253 2 1013
254 1 509
255 2 1021
256 0 257
257 279 2496329526...9292015617 (87 digits)
258 2 1033
259 38 71193377898497
260 1 521
261 1 523
262 0 263
263 29 141197049857
264 3 2113
265 2 1061
266 3 2129
267 2 1069
268 0 269
269 3 2153
270 0 271
271 4 4337
272 11 557057
273 1 547
274 2 1097
275 7 35201
276 0 277
277 2 1109
278 1 557
279 2 1117
280 0 281
281 1 563
282 0 283
283 30 303868936193
284 1 569
285 1 571
286 52 1288029493427961857
287 3 2297
288 1 577
289 10 295937
290 5 9281
291 4 4657
292 0 293
293 1 587
294 7 37633
295 2 1181
296 1 593
297 3 2377
298 2 1193
299 1 599
300 1 601
301 4 4817
302 3 2417
303 1 607
304 2 1217
305 3 2441
306 0 307
307 2 1229
308 1 617
309 1 619
310 0 311
311 9 159233
312 0 313
313 4 5009
314 7 40193
315 1 631
316 0 317
317 7 40577
318 5 10177
319 2 1277
320 1 641
321 1 643
322 2 1289
323 1 647
324 2 1297
325 2 1301
326 1 653
327 3 2617
328 8 83969
329 1 659
330 0 331
331 4 5297
332 3 2657
333 5 10657
334 6 21377
335 19 175636481
336 0 337
337 4 5393
338 1 677
339 3 2713
340 2 1361
341 1 683
342 7 43777
343 2 1373
344 3 2753
345 1 691
346 0 347
347 3 2777
348 0 349
349 10 357377
350 1 701
351 12 1437697
352 0 353
353 21 740294657
354 1 709
355 6 22721
356 5 11393
357 2 1429
358 0 359
359 1 719
360 6 23041
361 28 96905199617
362 3 2897
363 1 727
364 6 23297
365 5 11681
366 0 367
367 12 1503233
368 5 11777
369 1 739
370 2 1481
371 1 743
372 0 373
373 2 1493
374 5 11969
375 1 751
376 580 1487939695...6574002177 (178 digits)
377 11 772097
378 0 379
379 14 6209537
380 1 761
381 3 3049
382 0 383
383 6393 1169394518...1620750337 (1928 digits)
384 1 769
385 8 98561
386 1 773
387 2 1549
388 0 389
389 11 796673
390 3 3121
391 4 6257
392 3 3137
393 1 787
394 14 6455297
395 5 12641
396 0 397
397 4 6353
398 1 797
399 2 1597
400 0 401
</pre>
=={{header|PARI/GP}}==
{{trans|Julia}}
<syntaxhighlight lang="PARI/GP">
/* Check if there is an m such that n * 2^m + 1 is prime */
n2m1(n) = {
for(m = 0, 10^300,
if(isprime(n * 2^m + 1), return([1, m]));
);
return([0, 0]);
}
{
print(" N M Prime\n------------------");
for(n = 1, 400,
result = n2m1(n);
if(result[1],
print(Str(n) " " Str(result[2]) " " n * 2^result[2] + 1);
);
);
}
</syntaxhighlight>
{{out}}
<pre style="height:12ex;overflow:scroll;">
N M Prime
------------------
1 0 2
2 0 3
3 1 7
4 0 5
5 1 11
6 0 7
7 2 29
8 1 17
9 1 19
10 0 11
11 1 23
12 0 13
13 2 53
14 1 29
15 1 31
16 0 17
17 3 137
18 0 19
19 6 1217
20 1 41
21 1 43
22 0 23
23 1 47
24 2 97
25 2 101
26 1 53
27 2 109
28 0 29
29 1 59
30 0 31
31 8 7937
32 3 257
33 1 67
34 2 137
35 1 71
36 0 37
37 2 149
38 5 1217
39 1 79
40 0 41
41 1 83
42 0 43
43 2 173
44 1 89
45 2 181
46 0 47
47 583 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
48 1 97
49 2 197
50 1 101
51 1 103
52 0 53
53 1 107
54 1 109
55 4 881
56 1 113
57 2 229
58 0 59
59 5 1889
60 0 61
61 4 977
62 7 7937
63 1 127
64 2 257
65 1 131
66 0 67
67 2 269
68 1 137
69 1 139
70 0 71
71 3 569
72 0 73
73 2 293
74 1 149
75 1 151
76 4 1217
77 3 617
78 0 79
79 2 317
80 3 641
81 1 163
82 0 83
83 1 167
84 2 337
85 4 1361
86 1 173
87 2 349
88 0 89
89 1 179
90 1 181
91 8 23297
92 7 11777
93 2 373
94 582 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
95 1 191
96 0 97
97 2 389
98 1 197
99 1 199
100 0 101
101 3 809
102 0 103
103 16 6750209
104 5 3329
105 1 211
106 0 107
107 3 857
108 0 109
109 6 6977
110 3 881
111 1 223
112 0 113
113 1 227
114 1 229
115 2 461
116 1 233
117 3 937
118 4 1889
119 1 239
120 1 241
121 8 30977
122 3 977
123 6 7873
124 6 7937
125 1 251
126 0 127
127 2 509
128 1 257
129 3 1033
130 0 131
131 1 263
132 4 2113
133 4 2129
134 1 269
135 1 271
136 0 137
137 3 1097
138 0 139
139 2 557
140 1 281
141 1 283
142 2 569
143 53 1288029493427961857
144 2 577
145 6 9281
146 1 293
147 8 37633
148 0 149
149 3 1193
150 0 151
151 4 2417
152 3 1217
153 1 307
154 2 617
155 1 311
156 0 157
157 8 40193
158 1 317
159 6 10177
160 2 641
161 3 1289
162 0 163
163 2 653
164 9 83969
165 1 331
166 0 167
167 7 21377
168 1 337
169 2 677
170 3 1361
171 8 43777
172 0 173
173 1 347
174 1 349
175 2 701
176 1 353
177 2 709
178 0 179
179 1 359
180 0 181
181 4 2897
182 7 23297
183 1 367
184 6 11777
185 3 1481
186 1 373
187 6 11969
188 581 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
189 1 379
190 0 191
191 1 383
192 0 193
193 2 773
194 1 389
195 4 3121
196 0 197
197 15 6455297
198 0 199
199 2 797
200 1 401
201 3 1609
202 2 809
203 13 1662977
204 1 409
205 2 821
206 15 6750209
207 2 829
208 4 3329
209 1 419
210 0 211
211 20 221249537
212 3 1697
213 2 853
214 2 857
215 1 431
216 1 433
217 66 16011773855979890802689
218 5 6977
219 1 439
220 2 881
221 1 443
222 0 223
223 8 57089
224 1 449
225 3 1801
226 0 227
227 11 464897
228 0 229
229 6 14657
230 1 461
231 1 463
232 0 233
233 1 467
234 2 937
235 2 941
236 3 1889
237 4 3793
238 0 239
239 1 479
240 0 241
241 36 16561393893377
242 7 30977
243 1 487
244 2 977
245 1 491
246 5 7873
247 6 15809
248 5 7937
249 1 499
250 0 251
251 1 503
252 2 1009
253 2 1013
254 1 509
255 2 1021
256 0 257
257 279 249632952651006185613150855026822179503549278818199928480857894651449200648869292015617
258 2 1033
259 38 71193377898497
260 1 521
261 1 523
262 0 263
263 29 141197049857
264 3 2113
265 2 1061
266 3 2129
267 2 1069
268 0 269
269 3 2153
270 0 271
271 4 4337
272 11 557057
273 1 547
274 2 1097
275 7 35201
276 0 277
277 2 1109
278 1 557
279 2 1117
280 0 281
281 1 563
282 0 283
283 30 303868936193
284 1 569
285 1 571
286 52 1288029493427961857
287 3 2297
288 1 577
289 10 295937
290 5 9281
291 4 4657
292 0 293
293 1 587
294 7 37633
295 2 1181
296 1 593
297 3 2377
298 2 1193
299 1 599
300 1 601
301 4 4817
302 3 2417
303 1 607
304 2 1217
305 3 2441
306 0 307
307 2 1229
308 1 617
309 1 619
310 0 311
311 9 159233
312 0 313
313 4 5009
314 7 40193
315 1 631
316 0 317
317 7 40577
318 5 10177
319 2 1277
320 1 641
321 1 643
322 2 1289
323 1 647
324 2 1297
325 2 1301
326 1 653
327 3 2617
328 8 83969
329 1 659
330 0 331
331 4 5297
332 3 2657
333 5 10657
334 6 21377
335 19 175636481
336 0 337
337 4 5393
338 1 677
339 3 2713
340 2 1361
341 1 683
342 7 43777
343 2 1373
344 3 2753
345 1 691
346 0 347
347 3 2777
348 0 349
349 10 357377
350 1 701
351 12 1437697
352 0 353
353 21 740294657
354 1 709
355 6 22721
356 5 11393
357 2 1429
358 0 359
359 1 719
360 6 23041
361 28 96905199617
362 3 2897
363 1 727
364 6 23297
365 5 11681
366 0 367
367 12 1503233
368 5 11777
369 1 739
370 2 1481
371 1 743
372 0 373
373 2 1493
374 5 11969
375 1 751
376 580 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
377 11 772097
378 0 379
379 14 6209537
380 1 761
381 3 3049
382 0 383
383 6393 11693945185971565896920916176753769281418376445302724140914106576604960252116205468905429628661873192664799900323401294531072465400997845029722990758855393414014415817179228695517839305455702961095094596926622802342799137107509767542153683280899327558274011281588755909890607960835140712630830933978801393590855371457894042968287926562847826310125559303901351824980311279986492793008248059208985097459095049075732193161126922389950080848742183055141518931962329796357335158955758486061360294773463111842316561192036096585088267052290025273980611139612478214293303564141730470933187279751846912161098280963960686648202780382930927114525552446602357404550468641236474238897222372272898562140228039886991631673186995098587756569010989657598363351856992206826342175536967926902668804937341514786382018872919876784539436965319822540039220122728568129762675989071883516915894567537630751801497223803135172643203770169327233350522822938630733126833423559124391441973547309619943019237705312515304113424366223388373606440335025932390399945086075175009569272136997988977568262327875607690344516747889133920438003737328060362069562108376086129279385800262195985974144460914705464874882401864174074796383557151951711000378565395148939760434428093058777242253682181813425273399277638142811972296863003382484684788329148214958434057306251885787781329925372401240556666727438408378656900945061970219566055969587385482421092779185798692904507774583223151161566406541599486350580593707153172641891804260963429951215526999443852964537303345106153870841180251403751871193132336680841124129779119999935597712685839886558769823834654994044516702436738265181698869580022472787153167463772595005393815295009535991557511340157179280662197799109181549751673455040271529561595718940092424231253150263268513067972937042222806102175350331146290864120703025608712817763221723427454002746818270565050919821097445991953785331131470462682015972815241620750337
384 1 769
385 8 98561
386 1 773
387 2 1549
388 0 389
389 11 796673
390 3 3121
391 4 6257
392 3 3137
393 1 787
394 14 6455297
395 5 12641
396 0 397
397 4 6353
398 1 797
399 2 1597
400 0 401
</pre>
Line 1,475 ⟶ 2,644:
<!--</syntaxhighlight>-->
Output same as Wren (plus a few not particularly helpful digit counts).
=={{header|Python}}==
{{libheader|gmpy2}}
{{trans|Nim}}
<syntaxhighlight lang="python" line> # primesn2m1.py by Xing216
from gmpy2 import is_prime, mpz
print(" n m prime")
for n in range(1, 401):
m = 0
term = mpz(n)
while True:
if is_prime(term + 1):
print(f"{n:3d} {m} {term + 1:5d}")
break
m += 1
term *= 2
}</syntaxhighlight>
{{out}}
<pre style="height:20ex">
n m prime
1 0 2
2 0 3
3 1 7
4 0 5
5 1 11
6 0 7
7 2 29
8 1 17
9 1 19
10 0 11
11 1 23
12 0 13
13 2 53
14 1 29
15 1 31
16 0 17
17 3 137
18 0 19
19 6 1217
20 1 41
21 1 43
22 0 23
23 1 47
24 2 97
25 2 101
26 1 53
27 2 109
28 0 29
29 1 59
30 0 31
31 8 7937
32 3 257
33 1 67
34 2 137
35 1 71
36 0 37
37 2 149
38 5 1217
39 1 79
40 0 41
41 1 83
42 0 43
43 2 173
44 1 89
45 2 181
46 0 47
47 583 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
48 1 97
49 2 197
50 1 101
51 1 103
52 0 53
53 1 107
54 1 109
55 4 881
56 1 113
57 2 229
58 0 59
59 5 1889
60 0 61
61 4 977
62 7 7937
63 1 127
64 2 257
65 1 131
66 0 67
67 2 269
68 1 137
69 1 139
70 0 71
71 3 569
72 0 73
73 2 293
74 1 149
75 1 151
76 4 1217
77 3 617
78 0 79
79 2 317
80 3 641
81 1 163
82 0 83
83 1 167
84 2 337
85 4 1361
86 1 173
87 2 349
88 0 89
89 1 179
90 1 181
91 8 23297
92 7 11777
93 2 373
94 582 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
95 1 191
96 0 97
97 2 389
98 1 197
99 1 199
100 0 101
101 3 809
102 0 103
103 16 6750209
104 5 3329
105 1 211
106 0 107
107 3 857
108 0 109
109 6 6977
110 3 881
111 1 223
112 0 113
113 1 227
114 1 229
115 2 461
116 1 233
117 3 937
118 4 1889
119 1 239
120 1 241
121 8 30977
122 3 977
123 6 7873
124 6 7937
125 1 251
126 0 127
127 2 509
128 1 257
129 3 1033
130 0 131
131 1 263
132 4 2113
133 4 2129
134 1 269
135 1 271
136 0 137
137 3 1097
138 0 139
139 2 557
140 1 281
141 1 283
142 2 569
143 53 1288029493427961857
144 2 577
145 6 9281
146 1 293
147 8 37633
148 0 149
149 3 1193
150 0 151
151 4 2417
152 3 1217
153 1 307
154 2 617
155 1 311
156 0 157
157 8 40193
158 1 317
159 6 10177
160 2 641
161 3 1289
162 0 163
163 2 653
164 9 83969
165 1 331
166 0 167
167 7 21377
168 1 337
169 2 677
170 3 1361
171 8 43777
172 0 173
173 1 347
174 1 349
175 2 701
176 1 353
177 2 709
178 0 179
179 1 359
180 0 181
181 4 2897
182 7 23297
183 1 367
184 6 11777
185 3 1481
186 1 373
187 6 11969
188 581 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
189 1 379
190 0 191
191 1 383
192 0 193
193 2 773
194 1 389
195 4 3121
196 0 197
197 15 6455297
198 0 199
199 2 797
200 1 401
201 3 1609
202 2 809
203 13 1662977
204 1 409
205 2 821
206 15 6750209
207 2 829
208 4 3329
209 1 419
210 0 211
211 20 221249537
212 3 1697
213 2 853
214 2 857
215 1 431
216 1 433
217 66 16011773855979890802689
218 5 6977
219 1 439
220 2 881
221 1 443
222 0 223
223 8 57089
224 1 449
225 3 1801
226 0 227
227 11 464897
228 0 229
229 6 14657
230 1 461
231 1 463
232 0 233
233 1 467
234 2 937
235 2 941
236 3 1889
237 4 3793
238 0 239
239 1 479
240 0 241
241 36 16561393893377
242 7 30977
243 1 487
244 2 977
245 1 491
246 5 7873
247 6 15809
248 5 7937
249 1 499
250 0 251
251 1 503
252 2 1009
253 2 1013
254 1 509
255 2 1021
256 0 257
257 279 249632952651006185613150855026822179503549278818199928480857894651449200648869292015617
258 2 1033
259 38 71193377898497
260 1 521
261 1 523
262 0 263
263 29 141197049857
264 3 2113
265 2 1061
266 3 2129
267 2 1069
268 0 269
269 3 2153
270 0 271
271 4 4337
272 11 557057
273 1 547
274 2 1097
275 7 35201
276 0 277
277 2 1109
278 1 557
279 2 1117
280 0 281
281 1 563
282 0 283
283 30 303868936193
284 1 569
285 1 571
286 52 1288029493427961857
287 3 2297
288 1 577
289 10 295937
290 5 9281
291 4 4657
292 0 293
293 1 587
294 7 37633
295 2 1181
296 1 593
297 3 2377
298 2 1193
299 1 599
300 1 601
301 4 4817
302 3 2417
303 1 607
304 2 1217
305 3 2441
306 0 307
307 2 1229
308 1 617
309 1 619
310 0 311
311 9 159233
312 0 313
313 4 5009
314 7 40193
315 1 631
316 0 317
317 7 40577
318 5 10177
319 2 1277
320 1 641
321 1 643
322 2 1289
323 1 647
324 2 1297
325 2 1301
326 1 653
327 3 2617
328 8 83969
329 1 659
330 0 331
331 4 5297
332 3 2657
333 5 10657
334 6 21377
335 19 175636481
336 0 337
337 4 5393
338 1 677
339 3 2713
340 2 1361
341 1 683
342 7 43777
343 2 1373
344 3 2753
345 1 691
346 0 347
347 3 2777
348 0 349
349 10 357377
350 1 701
351 12 1437697
352 0 353
353 21 740294657
354 1 709
355 6 22721
356 5 11393
357 2 1429
358 0 359
359 1 719
360 6 23041
361 28 96905199617
362 3 2897
363 1 727
364 6 23297
365 5 11681
366 0 367
367 12 1503233
368 5 11777
369 1 739
370 2 1481
371 1 743
372 0 373
373 2 1493
374 5 11969
375 1 751
376 580 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177
377 11 772097
378 0 379
379 14 6209537
380 1 761
381 3 3049
382 0 383
383 6393 11693945185971565896920916176753769281418376445302724140914106576604960252116205468905429628661873192664799900323401294531072465400997845029722990758855393414014415817179228695517839305455702961095094596926622802342799137107509767542153683280899327558274011281588755909890607960835140712630830933978801393590855371457894042968287926562847826310125559303901351824980311279986492793008248059208985097459095049075732193161126922389950080848742183055141518931962329796357335158955758486061360294773463111842316561192036096585088267052290025273980611139612478214293303564141730470933187279751846912161098280963960686648202780382930927114525552446602357404550468641236474238897222372272898562140228039886991631673186995098587756569010989657598363351856992206826342175536967926902668804937341514786382018872919876784539436965319822540039220122728568129762675989071883516915894567537630751801497223803135172643203770169327233350522822938630733126833423559124391441973547309619943019237705312515304113424366223388373606440335025932390399945086075175009569272136997988977568262327875607690344516747889133920438003737328060362069562108376086129279385800262195985974144460914705464874882401864174074796383557151951711000378565395148939760434428093058777242253682181813425273399277638142811972296863003382484684788329148214958434057306251885787781329925372401240556666727438408378656900945061970219566055969587385482421092779185798692904507774583223151161566406541599486350580593707153172641891804260963429951215526999443852964537303345106153870841180251403751871193132336680841124129779119999935597712685839886558769823834654994044516702436738265181698869580022472787153167463772595005393815295009535991557511340157179280662197799109181549751673455040271529561595718940092424231253150263268513067972937042222806102175350331146290864120703025608712817763221723427454002746818270565050919821097445991953785331131470462682015972815241620750337
384 1 769
385 8 98561
386 1 773
387 2 1549
388 0 389
389 11 796673
390 3 3121
391 4 6257
392 3 3137
393 1 787
394 14 6455297
395 5 12641
396 0 397
397 4 6353
398 1 797
399 2 1597
400 0 401
</pre>
=={{header|Raku}}==
First 382 in less than a second. 383 pushes the total accumulated time over 25 seconds.
Line 1,880 ⟶ 3,469:
399 2: 1597
400 0: 401</pre>
=={{header|RPL}}==
As big ints are limited to 499 digits, it is not possible to calculate the 47th prime number.
{{works with|HP|49}}
« <span style="color:red">{ }
1 45</span> '''FOR''' n
<span style="color:red">0</span>
'''WHILE''' <span style="color:red">2</span> OVER ^ n * <span style="color:red">1</span> + DUP ISPRIME? NOT '''REPEAT'''
DROP <span style="color:red">1</span> +
'''END'''
NIP +
'''NEXT'''
» '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: { 2 3 7 5 11 7 29 17 19 11 23 13 53 29 31 17 137 19 1217 41 43 23 47 97 101 53 109 29 59 31 7937 257 67 137 71 37 149 1217 79 41 83 43 173 89 181 }
</pre>
=={{header|Sidef}}==
{{trans|Perl}}
Takes ~2 seconds to run.
<syntaxhighlight lang="ruby" line>for n in (1..400) {
var p = (^Inf -> lazy.map {|m| [m, n * 2**m + 1] }.first_by { .tail.is_prime })
printf("%3s %4s: %s\n", n, p...)
}</syntaxhighlight>
(same output as the Perl version)
=={{header|Wren}}==
{{libheader|Wren-gmp}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
| |||