List of Prime Numbers from 1 to 1000 & Effective Methods to Find Them

A prime number is a positive number that has only two factors: 1 and itself. This means it can only be divided exactly by 1 and the number itself. For example, 2, 3, 5, and 7 are prime numbers. These numbers are part of the group called natural numbers. However, 1 is not a prime number because it has only one factor, which is 1. Also, 0 is not a prime number because it is not a positive number and has unlimited factors.

In math, natural numbers follow five important rules, known as properties:

1. Closure Property – Adding or multiplying two natural numbers gives another natural number.
2. Commutative Property – You can change the order of numbers in addition or multiplication.
3. Associative Property – The grouping of numbers doesn’t affect the result in addition or multiplication.
4. Multiplicative Identity Property – Adding 0 or multiplying by 1 keeps the number the same.
5. Distributive Property – This helps in multiplying a number with a sum (like a × (b + c) = ab + ac).

To list out prime numbers from 1 to 1000, we need to know how we can classify a number as prime.

The number 13 has only two divisors of 1 and 13.

13/1=13

13/13=1

So 13 is a prime number.

The number 15 has divisors of 1, 3, 5, and 15 because:

15/1=15

15/3=5

15/5=3

15/15=1

So 15 is not a prime number.

By following the same rules to find out the prime numbers we can list out all prime numbers from 1 to 1000.

List of Prime Numbers from 1 to 1000?

There is a total of 168 prime numbers from 1 to 1000 which are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, and 997.

Numbers	Number of prime numbers
1 to 100	25 prime numbers
101-200	21 prime numbers
201-300	16 prime numbers
301-400	16 prime numbers
401-500	17 prime numbers
501-600	14 prime numbers
601-700	16 prime numbers
701-800	14 prime numbers
801-900	15 prime numbers
901-1000	14 prime numbers
Total	168

The steps given below can be used to find prime numbers from 1 to 1000 using Divisibility Test:

Step 1: To start, divide it by two. Utilize the two divisibility tests.

Step 2: See if you get a whole number. If you do, it can’t be a prime number.

Step 3: If you are unable to divide your result into a whole number, try using the following prime numbers instead: 3, 5, 7, 11 (not by 9 as 9 is divisible by 3), and so on, always using prime numbers. Try to get a whole number if you can. It cannot be a prime number if you do.

How to Find Prime Numbers Greater than 40?

We can list out all the prime numbers greater than 40 by using the formula n2+n+41. All you need to do is put all the whole numbers in place of ‘n’ one by one.

However, this formula will only give you all the prime numbers greater than 40.

Put n = 0,

Put n = 1,

Put n = 2,

Learn about Prime Numbers 1 to 100

How to Find Prime Numbers using the Sieve of Eratosthenes Method?

Sieve of Eratosthenes came up with a fantastic way to find all prime numbers that are up to a certain value. Its foundation is the idea of sieving (sifting) composite numbers, hence the name “Sieve of Eratosthenes.” Check out this illustration of Sieve of Eratosthenes.

• Circle the number 2, since it is the first prime number, and then erase all its higher multiples, namely all the composite even numbers.
• Move on to the next non-erased number, the number 3. Erase all its higher multiples of 3 too.
• Repeat the same texts for the next non-erased numbers.

List of Prime Numbers 1 to 1000

Following is the list of prime numbers from 1 to 1000:

Sequence	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

Learn about Odd composite numbers and Even Composite Numbers

Properties of Prime Numbers

Some of the important properties of prime numbers are given below:

• A prime number is a composite number greater than 1. Hence, while dividing the prime number we always get the reminder 1.
• Prime Numbers has exactly two factors, that is, 1 and the number itself.
• There is one and only one even prime number, that is, 2.
• 1 is neither prime nor composite.
• When a set of integers or numbers has only the number 1 as the common factor then they are known as Co-Prime Numbers. Hence, any two prime numbers are always co-prime to each other.
• Every number can be expressed as the product of prime numbers.
• Every even integer bigger than 2 can be split into two prime numbers, such as 6 = 3 + 3 or 8 = 3 + 5.

Learn about Smallest composite numbers and Largest composite numbers

Applications of Prime Numbers

Here are some of the daily life applications of prime numbers:

• When it comes to cyber-age security, we frequently employ and rely on prime numbers.
• We utilize the unique mathematical property of primes for encryption and decryption.
• To create error-correcting codes for use in communications, Prime Numbers are used. They make sure that automatic message correction is delivered and received.
• The foundation for developing public-key cryptography techniques is in the usage of prime numbers.
• Prime Numbers are employed in hash tables.
• They can also be employed to produce pseudorandom numbers.
• The design of rotor machines also makes use of primes. A number on one rotor is either coprime or prime to the number on another rotor. By doing so, the entire cycle can be generated before trying any different rotor positions.
• The RSA encryption technology uses primes for computing.

Difference Between Prime Numbers and Composite Numbers

Depending on how many factors they have, prime and composite numbers are different from one another.

Prime Numbers	Composite Numbers
Prime Numbers have only two factors, 1 and the number itself.	Composite numbers can have more than two factors.
Prime number pairs always make coprime numbers.	Any two even numbers can never be co-prime numbers.
Prime numbers are always odd numbers, except 2.	Composite numbers can be even or odd depending upon the factors they have.
Prime Numbers have prime factors except 1 which is neither prime nor composite.	If a composite number has a minimum of one even number, it will be an even number. If it has no even number in its factors, then it will be an odd number.
Prime numbers become rarer and rarer as numbers get larger.	Composite numbers are more as the number line moves towards the right.

Solved Examples 

Here are some solved examples of Prime Numbers 1 to 100 for you to prepare for your exam.

Example 1: Find if 57 is a prime number.

Solution: By the division method, we find that 1, 3, 19, and 57 divide 57.

For a number to be a prime number, a number should have only 2 factors, i.e., 1 and the number itself. We can see that 57 has more than 2 factors. Therefore, 57 is not a prime number. Also, 57 could not be represented in the form of 6n+1 where n = 1, 2, 3 ….

Therefore, 57 is not a prime number.

Example 2: Is 51 a prime number?

Solution: Let’s use the divisibility test on 51.

Divisibility Test of 2: It does not end with 0, 2, 4, 6, or 8. Hence, it is not divisible by 2.

Divisibility Test of 3: To check the divisibility by 3, we need to add the digits of the number 51. 5 + 1 = 6. 6 is divisible by 3. Hence, 51 is divisible by 3. 3 x 17 = 51

Thus, 51 is not a prime number because it can be divided by 3 and 17, as well as by itself and 1. ie it has four factors.

Example 3: List out twin prime numbers between 1 to 1000.

Solution: The list of twin prime numbers from 1 to 1000 is given here.

Twin prime numbers from 1 to 50: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43)

Twin prime numbers from 51 to 100: (59, 61), (71, 73)

Twin prime numbers from 101 to 200: (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199)

Twin prime numbers from 201 to 300: (227, 229), (239, 241), (269, 271), (281, 283)

Twin prime numbers from 301 to 400: (311, 313), (347, 349)

Twin prime numbers from 401 to 500: (419, 421), (431, 433), (461, 463)

Twin prime numbers from 501 to 1000: (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661), (809, 811), (821, 823), (827, 829), (857, 859), (881, 883)

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