Primes: n*2^m+1

Task

• Find and display the first 45 (n) primes of the form n × 2^m + 1 where m is the smallest valid non-negative integer.

Stretch

• Find and display the first 50 (n) primes of the form n × 2^m + 1 where m is the smallest valid non-negative integer.

Stretch harder

• Find and display the first 400 (n) primes of the form n × 2^m + 1 where m is the smallest valid non-negative integer.

See also

A050921 - Smallest prime of form n*2^m+1

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