Primes: n*2^m+1: Difference between revisions
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Primes with more than |
Primes with more than 40 digits have been (mercifully) abbreviated. |
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N M Prime |
N M Prime |
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Revision as of 08:53, 24 September 2022
- Task
- Find and display the first 45 (n) primes of the form n × 2m + 1 where m is the smallest valid non-negative integer.
- Stretch
- Find and display the first 50 (n) primes of the form n × 2m + 1 where m is the smallest valid non-negative integer.
- Stretch harder
- Find and display the first 400 (n) primes of the form n × 2m + 1 where m is the smallest valid non-negative integer.
- See also
A050921 - Smallest prime of form n*2^m+1
Julia
""" Rosetta code task: rosettacode.org/wiki/Primes:_n*2%5Em%2B1 """
using Primes
""" Return true if there is an m such that n * 2**m + 1 is prime """
function n2m1(n)
for m in big"0":big"10"^300
isprime(n * big"2"^m + 1) && return true, m
end
return false, 0
end
println(" N M Prime\n------------------")
for n in 1:400
tf, m = n2m1(n)
tf && println(lpad(n, 5), lpad(m, 5), " ", n * big"2"^m + 1)
end
- Output:
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
Raku
First 382 in less than a second. 383 pushes the total accumulated time over 25 seconds.
-> $n { (^∞).map: -> $m { if (my $p = $n × 2 ** $m + 1).is-prime { say "$n: $p"; last } } } for 1..400
- Output:
1: 2 2: 3 3: 7 4: 5 5: 11 6: 7 7: 29 8: 17 9: 19 10: 11 11: 23 12: 13 13: 53 14: 29 15: 31 16: 17 17: 137 18: 19 19: 1217 20: 41 21: 43 22: 23 23: 47 24: 97 25: 101 26: 53 27: 109 28: 29 29: 59 30: 31 31: 7937 32: 257 33: 67 34: 137 35: 71 36: 37 37: 149 38: 1217 39: 79 40: 41 41: 83 42: 43 43: 173 44: 89 45: 181 46: 47 47: 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177 48: 97 49: 197 50: 101 51: 103 52: 53 53: 107 54: 109 55: 881 56: 113 57: 229 58: 59 59: 1889 60: 61 61: 977 62: 7937 63: 127 64: 257 65: 131 66: 67 67: 269 68: 137 69: 139 70: 71 71: 569 72: 73 73: 293 74: 149 75: 151 76: 1217 77: 617 78: 79 79: 317 80: 641 81: 163 82: 83 83: 167 84: 337 85: 1361 86: 173 87: 349 88: 89 89: 179 90: 181 91: 23297 92: 11777 93: 373 94: 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177 95: 191 96: 97 97: 389 98: 197 99: 199 100: 101 101: 809 102: 103 103: 6750209 104: 3329 105: 211 106: 107 107: 857 108: 109 109: 6977 110: 881 111: 223 112: 113 113: 227 114: 229 115: 461 116: 233 117: 937 118: 1889 119: 239 120: 241 121: 30977 122: 977 123: 7873 124: 7937 125: 251 126: 127 127: 509 128: 257 129: 1033 130: 131 131: 263 132: 2113 133: 2129 134: 269 135: 271 136: 137 137: 1097 138: 139 139: 557 140: 281 141: 283 142: 569 143: 1288029493427961857 144: 577 145: 9281 146: 293 147: 37633 148: 149 149: 1193 150: 151 151: 2417 152: 1217 153: 307 154: 617 155: 311 156: 157 157: 40193 158: 317 159: 10177 160: 641 161: 1289 162: 163 163: 653 164: 83969 165: 331 166: 167 167: 21377 168: 337 169: 677 170: 1361 171: 43777 172: 173 173: 347 174: 349 175: 701 176: 353 177: 709 178: 179 179: 359 180: 181 181: 2897 182: 23297 183: 367 184: 11777 185: 1481 186: 373 187: 11969 188: 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177 189: 379 190: 191 191: 383 192: 193 193: 773 194: 389 195: 3121 196: 197 197: 6455297 198: 199 199: 797 200: 401 201: 1609 202: 809 203: 1662977 204: 409 205: 821 206: 6750209 207: 829 208: 3329 209: 419 210: 211 211: 221249537 212: 1697 213: 853 214: 857 215: 431 216: 433 217: 16011773855979890802689 218: 6977 219: 439 220: 881 221: 443 222: 223 223: 57089 224: 449 225: 1801 226: 227 227: 464897 228: 229 229: 14657 230: 461 231: 463 232: 233 233: 467 234: 937 235: 941 236: 1889 237: 3793 238: 239 239: 479 240: 241 241: 16561393893377 242: 30977 243: 487 244: 977 245: 491 246: 7873 247: 15809 248: 7937 249: 499 250: 251 251: 503 252: 1009 253: 1013 254: 509 255: 1021 256: 257 257: 249632952651006185613150855026822179503549278818199928480857894651449200648869292015617 258: 1033 259: 71193377898497 260: 521 261: 523 262: 263 263: 141197049857 264: 2113 265: 1061 266: 2129 267: 1069 268: 269 269: 2153 270: 271 271: 4337 272: 557057 273: 547 274: 1097 275: 35201 276: 277 277: 1109 278: 557 279: 1117 280: 281 281: 563 282: 283 283: 303868936193 284: 569 285: 571 286: 1288029493427961857 287: 2297 288: 577 289: 295937 290: 9281 291: 4657 292: 293 293: 587 294: 37633 295: 1181 296: 593 297: 2377 298: 1193 299: 599 300: 601 301: 4817 302: 2417 303: 607 304: 1217 305: 2441 306: 307 307: 1229 308: 617 309: 619 310: 311 311: 159233 312: 313 313: 5009 314: 40193 315: 631 316: 317 317: 40577 318: 10177 319: 1277 320: 641 321: 643 322: 1289 323: 647 324: 1297 325: 1301 326: 653 327: 2617 328: 83969 329: 659 330: 331 331: 5297 332: 2657 333: 10657 334: 21377 335: 175636481 336: 337 337: 5393 338: 677 339: 2713 340: 1361 341: 683 342: 43777 343: 1373 344: 2753 345: 691 346: 347 347: 2777 348: 349 349: 357377 350: 701 351: 1437697 352: 353 353: 740294657 354: 709 355: 22721 356: 11393 357: 1429 358: 359 359: 719 360: 23041 361: 96905199617 362: 2897 363: 727 364: 23297 365: 11681 366: 367 367: 1503233 368: 11777 369: 739 370: 1481 371: 743 372: 373 373: 1493 374: 11969 375: 751 376: 1487939695262196876907983166454197495251350196192890428923003345454869706240895712896623468784438158657419591298913094265537812046389415279164757669092989298186306341246574002177 377: 772097 378: 379 379: 6209537 380: 761 381: 3049 382: 383 383: 11693945185971565896920916176753769281418376445302724140914106576604960252116205468905429628661873192664799900323401294531072465400997845029722990758855393414014415817179228695517839305455702961095094596926622802342799137107509767542153683280899327558274011281588755909890607960835140712630830933978801393590855371457894042968287926562847826310125559303901351824980311279986492793008248059208985097459095049075732193161126922389950080848742183055141518931962329796357335158955758486061360294773463111842316561192036096585088267052290025273980611139612478214293303564141730470933187279751846912161098280963960686648202780382930927114525552446602357404550468641236474238897222372272898562140228039886991631673186995098587756569010989657598363351856992206826342175536967926902668804937341514786382018872919876784539436965319822540039220122728568129762675989071883516915894567537630751801497223803135172643203770169327233350522822938630733126833423559124391441973547309619943019237705312515304113424366223388373606440335025932390399945086075175009569272136997988977568262327875607690344516747889133920438003737328060362069562108376086129279385800262195985974144460914705464874882401864174074796383557151951711000378565395148939760434428093058777242253682181813425273399277638142811972296863003382484684788329148214958434057306251885787781329925372401240556666727438408378656900945061970219566055969587385482421092779185798692904507774583223151161566406541599486350580593707153172641891804260963429951215526999443852964537303345106153870841180251403751871193132336680841124129779119999935597712685839886558769823834654994044516702436738265181698869580022472787153167463772595005393815295009535991557511340157179280662197799109181549751673455040271529561595718940092424231253150263268513067972937042222806102175350331146290864120703025608712817763221723427454002746818270565050919821097445991953785331131470462682015972815241620750337 384: 769 385: 98561 386: 773 387: 1549 388: 389 389: 796673 390: 3121 391: 6257 392: 3137 393: 787 394: 6455297 395: 12641 396: 397 397: 6353 398: 797 399: 1597 400: 401
Wren
import "./gmp" for Mpz
import "./fmt" for Fmt
System.print(" N M Prime")
System.print("------------------")
for (n in 1..400) {
var m = 0
while (true) {
var p = Mpz.from(n).mul(Mpz.one.lsh(m)).add(1)
if (p.probPrime(15) > 0) {
Fmt.print("$3d $4d $20a", n, m, p)
break
}
m = m + 1
}
}- Output:
Primes with more than 40 digits have been (mercifully) abbreviated.
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 14879396952621968769...86306341246574002177 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 14879396952621968769...86306341246574002177 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 14879396952621968769...86306341246574002177 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 24963295265100618561...49200648869292015617 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 14879396952621968769...86306341246574002177 377 11 772097 378 0 379 379 14 6209537 380 1 761 381 3 3049 382 0 383 383 6393 11693945185971565896...15972815241620750337 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