Primes: n*2^m+1: Difference between revisions
Added Java
(Add PARI/GP implementation) |
(Added Java) |
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(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|Java}}==
Though it takes about 15 minutes to find the numbers up to 400 on my Windows 11 laptop, it can find all of them except 383 in a few seconds.<br/>
Tested with OpenJDK version 22.
<syntaxhighlight lang="java">
import java.math.BigInteger;
public class primesNx2ToMPlus1 // find primes of the form 1+n*2^m where m is
{ // the lowest integer >= 0 such that 1+n*2^m is prime
static final int maxM = 8000; // maximum m we will consider
public static void main( String[] args )
{
BigInteger nn = BigInteger.ZERO;
for( int n = 1; n <= 400; n ++ )
{
int m = 0;
BigInteger twoToM = BigInteger.ONE;
BigInteger p = BigInteger.ZERO;
boolean notFound = true;
nn = nn.add( BigInteger.ONE );
while( notFound && m <= maxM )
{
p = nn.multiply( twoToM ).add( BigInteger.ONE );
if( ( notFound = ! p.isProbablePrime( 10 ) ) )
{
twoToM = twoToM.add( twoToM );
m += 1;
}
}
System.out.print( String.format( "%3d", n ) );
if( notFound )
{
System.out.println( " not found" );
}
else
{
System.out.println( " " + String.format( "%6d", m ) + ": " + p.toString() );
}
}
} // main
} // primesNx2ToMPlus1
</syntaxhighlight>
{{out}}
As with many other samples, the long primes have been manually shortened.
<pre style="height:30ex;overflow:scroll;">
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: 148793969526...246574002177
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: 148793969526...246574002177
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: 148793969526...246574002177
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: 249632952651...869292015617
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: 148793969526...246574002177
377 11: 772097
378 0: 379
379 14: 6209537
380 1: 761
381 3: 3049
382 0: 383
383 6393: 116939451859...241620750337
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|jq}}==
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