List of Prime Numbers (1-5000)

Prime numbers are positive integers greater than 1 that lack divisors other than 1 and themselves. In simpler terms, a prime number is a natural number that cannot be generated by multiplying two smaller natural numbers. Notable examples of prime numbers include 2, 3, 5, 7, 11, 13, and so forth. For a comprehensive list, you can check all prime numbers ranging from 1 to 5000. 

A more formal definition is as follows: A positive integer p is classified as prime if its sole positive divisors are 1 and p itself. Conversely, if a positive integer n possesses divisors beyond 1 and itself, it is termed a composite number. For instance, 2 and 3 are prime numbers because their only divisors are 1 and 2, and 1 and 3, respectively. On the other hand, 4 is not a prime number as it has divisors 1, 2, and 4. 

Prime numbers hold a top position in number theory and find applications across various fields, including cryptography, computer science, and mathematics. The distribution of prime numbers, a intricate subject, has captivated mathematicians for centuries.

List of Prime Numbers from 1 to 5000 – Prime Numbers Explained

S.No	Prime Number
1	2
2	3
3	5
4	7
5	11
6	13
7	17
8	19
9	23
10	29
11	31
12	37
13	41
14	43
15	47
16	53
17	59
18	61
19	67
20	71
21	73
22	79
23	83
24	89
25	97
26	101
27	103
28	107
29	109
30	113
31	127
32	131
33	137
34	139
35	149
36	151
37	157
38	163
39	167
40	173
41	179
42	181
43	191
44	193
45	197
46	199
47	211
48	223
49	227
50	229
51	233
52	239
53	241
54	251
55	257
56	263
57	269
58	271
59	277
60	281
61	283
62	293
63	307
64	311
65	313
66	317
67	331
68	337
69	347
70	349
71	353
72	359
73	367
74	373
75	379
76	383
77	389
78	397
79	401
80	409
81	419
82	421
83	431
84	433
85	439
86	443
87	449
88	457
89	461
90	463
91	467
92	479
93	487
94	491
95	499
96	503
97	509
98	521
99	523
100	541
101	547
102	557
103	563
104	569
105	571
106	577
107	587
108	593
109	599
110	601
111	607
112	613
113	617
114	619
115	631
116	641
117	643
118	647
119	653
120	659
121	661
122	673
123	677
124	683
125	691
126	701
127	709
128	719
129	727
130	733
131	739
132	743
133	751
134	757
135	761
136	769
137	773
138	787
139	797
140	809
141	811
142	821
143	823
144	827
145	829
146	839
147	853
148	857
149	859
150	863
151	877
152	881
153	883
154	887
155	907
156	911
157	919
158	929
159	937
160	941
161	947
162	953
163	967
164	971
165	977
166	983
167	991
168	997
169	1009
170	1013
171	1019
172	1021
173	1031
174	1033
175	1039
176	1049
177	1051
178	1061
179	1063
180	1069
181	1087
182	1091
183	1093
184	1097
185	1103
186	1109
187	1117
188	1123
189	1129
190	1151
191	1153
192	1163
193	1171
194	1181
195	1187
196	1193
197	1201
198	1213
199	1217
200	1223
201	1229
202	1231
203	1237
204	1249
205	1259
206	1277
207	1279
208	1283
209	1289
210	1291
211	1297
212	1301
213	1303
214	1307
215	1319
216	1321
217	1327
218	1361
219	1367
220	1373
221	1381
222	1399
223	1409
224	1423
225	1427
226	1429
227	1433
228	1439
229	1447
230	1451
231	1453
232	1459
233	1471
234	1481
235	1483
236	1487
237	1489
238	1493
239	1499
240	1511
241	1523
242	1531
243	1543
244	1549
245	1553
246	1559
247	1567
248	1571
249	1579
250	1583
251	1597
252	1601
253	1607
254	1609
255	1613
256	1619
257	1621
258	1627
259	1637
260	1657
261	1663
262	1667
263	1669
264	1693
265	1697
266	1699
267	1709
268	1721
269	1723
270	1733
271	1741
272	1747
273	1753
274	1759
275	1777
276	1783
277	1787
278	1789
279	1801
280	1811
281	1823
282	1831
283	1847
284	1861
285	1867
286	1871
287	1873
288	1877
289	1879
290	1889
291	1901
292	1907
293	1913
294	1931
295	1933
296	1949
297	1951
298	1973
299	1979
300	1987
301	1993
302	1997
303	1999
304	2003
305	2011
306	2017
307	2027
308	2029
309	2039
310	2053
311	2063
312	2069
313	2081
314	2083
315	2087
316	2089
317	2099
318	2111
319	2113
320	2129
321	2131
322	2137
323	2141
324	2143
325	2153
326	2161
327	2179
328	2203
329	2207
330	2213
331	2221
332	2237
333	2239
334	2243
335	2251
336	2267
337	2269
338	2273
339	2281
340	2287
341	2293
342	2297
343	2309
344	2311
345	2333
346	2339
347	2341
348	2347
349	2351
350	2357
351	2371
352	2377
353	2381
354	2383
355	2389
356	2393
357	2399
358	2411
359	2417
360	2423
361	2437
362	2441
363	2447
364	2459
365	2467
366	2473
367	2477
368	2503
369	2521
370	2531
371	2539
372	2543
373	2549
374	2551
375	2557
376	2579
377	2591
378	2593
379	2609
380	2617
381	2621
382	2633
383	2647
384	2657
385	2659
386	2663
387	2671
388	2677
389	2683
390	2687
391	2689
392	2693
393	2699
394	2707
395	2711
396	2713
397	2719
398	2729
399	2731
400	2741
401	2749
402	2753
403	2767
404	2777
405	2789
406	2791
407	2797
408	2801
409	2803
410	2819
411	2833
412	2837
413	2843
414	2851
415	2857
416	2861
417	2879
418	2887
419	2897
420	2903
421	2909
422	2917
423	2927
424	2939
425	2953
426	2957
427	2963
428	2969
429	2971
430	2999
431	3001
432	3011
433	3019
434	3023
435	3037
436	3041
437	3049
438	3061
439	3067
440	3079
441	3083
442	3089
443	3109
444	3119
445	3121
446	3137
447	3163
448	3167
449	3169
450	3181
451	3187
452	3191
453	3203
454	3209
455	3217
456	3221
457	3229
458	3251
459	3253
460	3257
461	3259
462	3271
463	3299
464	3301
465	3307
466	3313
467	3319
468	3323
469	3329
470	3331
471	3343
472	3347
473	3359
474	3361
475	3371
476	3373
477	3389
478	3391
479	3407
480	3413
481	3433
482	3449
483	3457
484	3461
485	3463
486	3467
487	3469
488	3491
489	3499
490	3511
491	3517
492	3527
493	3529
494	3533
495	3539
496	3541
497	3547
498	3557
499	3559
500	3571
501	3581
502	3583
503	3593
504	3607
505	3613
506	3617
507	3623
508	3631
509	3637
510	3643
511	3659
512	3671
513	3673
514	3677
515	3691
516	3697
517	3701
518	3709
519	3719
520	3727
521	3733
522	3739
523	3761
524	3767
525	3769
526	3779
527	3793
528	3797
529	3803
530	3821
531	3823
532	3833
533	3847
534	3851
535	3853
536	3863
537	3877
538	3881
539	3889
540	3907
541	3911
542	3917
543	3919
544	3923
545	3929
546	3931
547	3943
548	3947
549	3967
550	3989
551	4001
552	4003
553	4007
554	4013
555	4019
556	4021
557	4027
558	4049
559	4051
560	4057
561	4073
562	4079
563	4091
564	4093
565	4099
566	4111
567	4127
568	4129
569	4133
570	4139
571	4153
572	4157
573	4159
574	4177
575	4201
576	4211
577	4217
578	4219
579	4229
580	4231
581	4241
582	4243
583	4253
584	4259
585	4261
586	4271
587	4273
588	4283
589	4289
590	4297
591	4327
592	4337
593	4339
594	4349
595	4357
596	4363
597	4373
598	4391
599	4397
600	4409
601	4421
602	4423
603	4441
604	4447
605	4451
606	4457
607	4463
608	4481
609	4483
610	4493
611	4507
612	4513
613	4517
614	4519
615	4523
616	4547
617	4549
618	4561
619	4567
620	4583
621	4591
622	4597
623	4603
624	4621
625	4637
626	4639
627	4643
628	4649
629	4651
630	4657
631	4663
632	4673
633	4679
634	4691
635	4703
636	4721
637	4723
638	4729
639	4733
640	4751
641	4759
642	4783
643	4787
644	4789
645	4793
646	4799
647	4801
648	4813
649	4817
650	4831
651	4861
652	4871
653	4877
654	4889
655	4903
656	4909
657	4919
658	4931
659	4933
660	4937
661	4943
662	4951
663	4957
664	4967
665	4969
666	4973
667	4987
668	4993
669	4999

There are 669 prime numbers between 1 to 5000 and 2 is the first prime number. Why is 1 not a prime number? 1 is not a prime number because it has only one factor, namely 1.

Distinctive Features of Prime Numbers

• Uniqueness: Each positive integer greater than 1 can be uniquely represented as a product of prime numbers, irrespective of the order of the factors. This principle is recognized as the Fundamental Theorem of Arithmetic. 
• Infinitude of Primes: The set of prime numbers is infinite, as demonstrated by the ancient Greek mathematician Euclid around 300 BCE. His proof is a classic example of a proof by contradiction. 
• Prime Factorization: The process of determining the prime factorization of a number involves breaking it down into a product of prime factors. This technique is essential in various mathematical operations, including simplifying fractions and finding the greatest common divisor (GCD) of two numbers. 
• Twin Primes: Twin primes are pairs of prime numbers with a difference of 2, such as (3, 5), (11, 13), and (17, 19). The Twin Prime Conjecture suggests an infinite number of such pairs, although it remains unproven. 
• Prime Number Theorem: Formulated by mathematicians like Jacques Hadamard and Charles Jean de la Vallée-Poussin, the Prime Number Theorem describes the asymptotic distribution of prime numbers. It estimates how the density of prime numbers decreases as numbers grow larger. 
• Prime Numbers and Cryptography: Prime numbers play a pivotal role in modern cryptography, particularly in algorithms like RSA that depend on the challenge of factoring the product of two large prime numbers for secure internet communication. 
• Mersenne Primes: Mersenne primes are primes expressible in the form 2p – 1, where p is also a prime number. These primes exhibit a fascinating connection to perfect numbers and are extensively studied for their mathematical properties. 
• Prime Sieves: Prime sieves are algorithms designed for efficiently identifying all prime numbers up to a specified limit. The Sieve of Eratosthenes, a well-known prime sieve, is a straightforward method for prime identification. 
• Prime Gap: The prime gap refers to the difference between consecutive prime numbers. Despite the seeming randomness in prime distribution, there are still unresolved questions about the upper bounds of prime gaps. 
• Prime Number Patterns: While prime numbers themselves lack a predictable pattern (referred to as the "randomness" of primes), there are conjectures and patterns related to their distribution. However, proving these conjectures remains a challenging endeavor. 

Prime numbers continue to be a fertile area of exploration in mathematics, captivating researchers worldwide due to their distinct properties and far-reaching implications across various fields. 

Also Check

US Cities Name List

World Country Capitals List