1000 Prime Numbers

What Are Prime Numbers?

A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Prime numbers are the building blocks of mathematics and play a vital role in number theory, cryptography, computer science, and various mathematical calculations.

Examples of prime numbers include:

2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

The number 2 is the only even prime number because all other even numbers are divisible by 2.

First 1000 Prime Numbers

The table below contains the first 1000 prime numbers in ascending order. These prime numbers range from 2 to 7919 and are commonly used in mathematics, education, programming, and prime factorization calculations.

Whether you’re a student, teacher, researcher, or developer, this comprehensive prime number list provides a quick reference for identifying and working with prime numbers.

#	1	2	3	4	5	6	7	8	9	10
1-10	2	3	5	7	11	13	17	19	23	29
11-20	31	37	41	43	47	53	59	61	67	71
21-30	73	79	83	89	97	101	103	107	109	113
31-40	127	131	137	139	149	151	157	163	167	173
41-50	179	181	191	193	197	199	211	223	227	229
51-60	233	239	241	251	257	263	269	271	277	281
61-70	283	293	307	311	313	317	331	337	347	349
71-80	353	359	367	373	379	383	389	397	401	409
81-90	419	421	431	433	439	443	449	457	461	463
91-100	467	479	487	491	499	503	509	521	523	541
101-110	547	557	563	569	571	577	587	593	599	601
111-120	607	613	617	619	631	641	643	647	653	659
121-130	661	673	677	683	691	701	709	719	727	733
131-140	739	743	751	757	761	769	773	787	797	809
141-150	811	821	823	827	829	839	853	857	859	863
151-160	877	881	883	887	907	911	919	929	937	941
161-170	947	953	967	971	977	983	991	997	1009	1013
171-180	1019	1021	1031	1033	1039	1049	1051	1061	1063	1069
181-190	1087	1091	1093	1097	1103	1109	1117	1123	1129	1151
191-200	1153	1163	1171	1181	1187	1193	1201	1213	1217	1223
201-210	1229	1231	1237	1249	1259	1277	1279	1283	1289	1291
211-220	1297	1301	1303	1307	1319	1321	1327	1361	1367	1373
221-230	1381	1399	1409	1423	1427	1429	1433	1439	1447	1451
231-240	1453	1459	1471	1481	1483	1487	1489	1493	1499	1511
241-250	1523	1531	1543	1549	1553	1559	1567	1571	1579	1583
251-260	1597	1601	1607	1609	1613	1619	1621	1627	1637	1657
261-270	1663	1667	1669	1693	1697	1699	1709	1721	1723	1733
271-280	1741	1747	1753	1759	1777	1783	1787	1789	1801	1811
281-290	1823	1831	1847	1861	1867	1871	1873	1877	1879	1889
291-300	1901	1907	1913	1931	1933	1949	1951	1973	1979	1987
301-310	1993	1997	1999	2003	2011	2017	2027	2029	2039	2053
311-320	2063	2069	2081	2083	2087	2089	2099	2111	2113	2129
321-330	2131	2137	2141	2143	2153	2161	2179	2203	2207	2213
331-340	2221	2237	2239	2243	2251	2267	2269	2273	2281	2287
341-350	2293	2297	2309	2311	2333	2339	2341	2347	2351	2357
351-360	2371	2377	2381	2383	2389	2393	2399	2411	2417	2423
361-370	2437	2441	2447	2459	2467	2473	2477	2503	2521	2531
371-380	2539	2543	2549	2551	2557	2579	2591	2593	2609	2617
381-390	2621	2633	2647	2657	2659	2663	2671	2677	2683	2687
391-400	2689	2693	2699	2707	2711	2713	2719	2729	2731	2741
401-410	2749	2753	2767	2777	2789	2791	2797	2801	2803	2819
411-420	2833	2837	2843	2851	2857	2861	2879	2887	2897	2903
421-430	2909	2917	2927	2939	2953	2957	2963	2969	2971	2999
431-440	3001	3011	3019	3023	3037	3041	3049	3061	3067	3079
441-450	3083	3089	3109	3119	3121	3137	3163	3167	3169	3181
451-460	3187	3191	3203	3209	3217	3221	3229	3251	3253	3257
461-470	3259	3271	3299	3301	3307	3313	3319	3323	3329	3331
471-480	3343	3347	3359	3361	3371	3373	3389	3391	3407	3413
481-490	3433	3449	3457	3461	3463	3467	3469	3491	3499	3511
491-500	3517	3527	3529	3533	3539	3541	3547	3557	3559	3571
501-510	3581	3583	3593	3607	3613	3617	3623	3631	3637	3643
511-520	3659	3671	3673	3677	3691	3697	3701	3709	3719	3727
521-530	3733	3739	3761	3767	3769	3779	3793	3797	3803	3821
531-540	3823	3833	3847	3851	3853	3863	3877	3881	3889	3907
541-550	3911	3917	3919	3923	3929	3931	3943	3947	3967	3989
551-560	4001	4003	4007	4013	4019	4021	4027	4049	4051	4057
561-570	4073	4079	4091	4093	4099	4111	4127	4129	4133	4139
571-580	4153	4157	4159	4177	4201	4211	4217	4219	4229	4231
581-590	4241	4243	4253	4259	4261	4271	4273	4283	4289	4297
591-600	4327	4337	4339	4349	4357	4363	4373	4391	4397	4409
601-610	4421	4423	4441	4447	4451	4457	4463	4481	4483	4493
611-620	4507	4513	4517	4519	4523	4547	4549	4561	4567	4583
621-630	4591	4597	4603	4621	4637	4639	4643	4649	4651	4657
631-640	4663	4673	4679	4691	4703	4721	4723	4729	4733	4751
641-650	4759	4783	4787	4789	4793	4799	4801	4813	4817	4831
651-660	4861	4871	4877	4889	4903	4909	4919	4931	4933	4937
661-670	4943	4951	4957	4967	4969	4973	4987	4993	4999	5003
671-680	5009	5011	5021	5023	5039	5051	5059	5077	5081	5087
681-690	5099	5101	5107	5113	5119	5147	5153	5167	5171	5179
691-700	5189	5197	5209	5227	5231	5233	5237	5261	5273	5279
701-710	5281	5297	5303	5309	5323	5333	5347	5351	5381	5387
711-720	5393	5399	5407	5413	5417	5419	5431	5437	5441	5443
721-730	5449	5471	5477	5479	5483	5501	5503	5507	5519	5521
731-740	5527	5531	5557	5563	5569	5573	5581	5591	5623	5639
741-750	5641	5647	5651	5653	5657	5659	5669	5683	5689	5693
751-760	5701	5711	5717	5737	5741	5743	5749	5779	5783	5791
761-770	5801	5807	5813	5821	5827	5839	5843	5849	5851	5857
771-780	5861	5867	5869	5879	5881	5897	5903	5923	5927	5939
781-790	5953	5981	5987	6007	6011	6029	6037	6043	6047	6053
791-800	6067	6073	6079	6089	6091	6101	6113	6121	6131	6133
801-810	6143	6151	6163	6173	6197	6199	6203	6211	6217	6221
811-820	6229	6247	6257	6263	6269	6271	6277	6287	6299	6301
821-830	6311	6317	6323	6329	6337	6343	6353	6359	6361	6367
831-840	6373	6379	6389	6397	6421	6427	6449	6451	6469	6473
841-850	6481	6491	6521	6529	6547	6551	6553	6563	6569	6571
851-860	6577	6581	6599	6607	6619	6637	6653	6659	6661	6673
861-870	6679	6689	6691	6701	6703	6709	6719	6733	6737	6761
871-880	6763	6779	6781	6791	6793	6803	6823	6827	6829	6833
881-890	6841	6857	6863	6869	6871	6883	6899	6907	6911	6917
891-900	6947	6949	6959	6961	6967	6971	6977	6983	6991	6997
901-910	7001	7013	7019	7027	7039	7043	7057	7069	7079	7103
911-920	7109	7121	7127	7129	7151	7159	7177	7187	7193	7207
921-930	7211	7213	7219	7229	7237	7243	7247	7253	7283	7297
931-940	7307	7309	7321	7331	7333	7349	7351	7369	7393	7411
941-950	7417	7433	7451	7457	7459	7477	7481	7487	7489	7499
951-960	7507	7517	7523	7529	7537	7541	7547	7549	7559	7561
961-970	7573	7577	7583	7589	7591	7603	7607	7621	7639	7643
971-980	7649	7669	7673	7681	7687	7691	7699	7703	7717	7723
981-990	7727	7741	7753	7757	7759	7789	7793	7817	7823	7829
991-1000	7841	7853	7867	7873	7877	7879	7883	7901	7907	7919
1001-1009	7927	7933	7937	7949	7951	7963	7993	8009	8011

Understanding Prime Number Notation

The nth prime number is commonly represented as:

pₙ

Examples:

• p₁ = 2
• p₂ = 3
• p₃ = 5
• p₄ = 7
• p₅ = 11

Another standard notation is:

Prime[n]

Examples:

• Prime[1] = 2
• Prime[2] = 3
• Prime[3] = 5
• Prime[4] = 7
• Prime[5] = 11

Both notations refer to the same sequence of prime numbers.

How to Find the nth Prime Number

Finding the nth prime number is easy using a prime number lookup table.

For example, if you want to find:

Prime[223]

Locate:

• Row heading: 220
• Column heading: 3

Since:

223 = 220 + 3

The value at this position is:

Prime[223] = 1409

This method allows you to quickly locate any prime number within the first 1000 primes.

Why Prime Numbers Are Important

Prime numbers are essential in many areas, including:

• Prime factorization
• Number theory
• Mathematics education
• Computer algorithms
• Cybersecurity and encryption
• RSA cryptography
• Data security systems
• Competitive programming

Many modern encryption methods rely on large prime numbers to secure digital communications and financial transactions.

Verify Prime Numbers Instantly

Not sure whether a number is prime?

Use our Prime Factors Calculator to:

• Check if a number is prime or composite
• Find prime factors instantly
• Generate a factor tree
• Calculate the nth prime number
• Verify divisibility
• Learn step-by-step prime factorization

This makes it easy for students, educators, and professionals to work with prime numbers efficiently.

Frequently Asked Questions

What is the first prime number?

The first prime number is 2.

What is the 1000th prime number?

The 1000th prime number is 7919.

Is 1 a prime number?

No. A prime number must have exactly two positive divisors. The number 1 has only one divisor.

How do you find the prime factorization of a number?

To find the prime factorization of a number, divide it repeatedly by the smallest prime numbers (2, 3, 5, 7, etc.) until the result becomes 1. The product of all prime divisors gives the prime factorization.

For example:

60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

How do you get prime factorization on a calculator?

You can use a Prime Factorization Calculator by entering any positive integer and clicking the calculate button. The calculator instantly displays the prime factors, factor tree, and step-by-step factorization.

What are the prime numbers from 1 to 10?

The prime numbers between 1 and 10 are:

2, 3, 5, and 7

The numbers 1, 4, 6, 8, 9, and 10 are not prime because they have more than two factors.

What is a prime factor of 42?

The prime factors of 42 are:

2, 3, and 7

Prime factorization of 42:

42 = 2 × 3 × 7

How can I find prime factorization quickly?

The fastest way is to divide the number by the smallest possible prime number repeatedly. You can also use an online Prime Factorization Calculator for instant and accurate results.

What is the cube root of 2744?

The cube root of 2744 is:

∛2744 = 14

Because:

14 × 14 × 14 = 2744

Is 1000000000000066600000000000001 a prime number?

This is a very large number and requires advanced primality testing to determine whether it is prime or composite. Large integers are typically checked using specialized algorithms and software rather than manual calculations.

What is an easy trick to find prime numbers?

A simple trick is to test divisibility only by prime numbers less than or equal to the square root of the number. If no prime number divides it evenly, the number is prime.

Why is 69 not a prime number?

69 is not a prime number because it has factors other than 1 and itself.

69 = 3 × 23

Since it has more than two factors, it is a composite number.

How do you find the prime factorization of 60?

Divide 60 by the smallest prime numbers:

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

Prime factorization:

60 = 2² × 3 × 5

Is 21 a prime factor of 42?

No, 21 is not a prime factor because 21 itself is not a prime number.

21 = 3 × 7

The prime factors of 42 are 2, 3, and 7.

Is there an easy way to find factors?

Yes. Test divisibility from 1 up to the square root of the number. Whenever a number divides evenly, both the divisor and quotient are factors. Online factor calculators can find all factors instantly.

What is the best trick for prime factorization?

The most effective method is to start dividing by the smallest prime number possible and continue until the quotient becomes 1. A factor tree is another popular visual method for finding prime factorization quickly.

What is the difference between factors and prime factors?

Factors are numbers that divide a number exactly. Prime factors are factors that are also prime numbers.

For example, factors of 24 are:

1, 2, 3, 4, 6, 8, 12, 24

Prime factors of 24 are:

2 and 3

What is a factor tree?

A factor tree is a diagram that breaks a number into its prime factors. It helps students visualize the prime factorization process step by step.

Why is prime factorization important?

Prime factorization is used in mathematics, cryptography, algebra, fraction simplification, finding GCF and LCM, and many computer science applications.