1. 5th prime number

Solution:
Prime:1 = 2
Prime:2 = 3
Prime:3 = 5
Prime:4 = 7
Prime:5 = 11

The following lists the first 5 primes
2, 3, 5, 7, 11


So `5^(th)` prime number is 11

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2. 10th prime number

Solution:
Prime:1 = 2
Prime:2 = 3
Prime:3 = 5
Prime:4 = 7
Prime:5 = 11
Prime:6 = 13
Prime:7 = 17
Prime:8 = 19
Prime:9 = 23
Prime:10 = 29

The following lists the first 10 primes
2, 3, 5, 7, 11, 13, 17, 19, 23, 29


So `10^(th)` prime number is 29

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3. 25th prime number

Solution:

The following lists the first 25 primes
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

The following table lists the first 25 primes, with 10 columns of consecutive primes in each of the 3 rows

	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

So `25^(th)` prime number is 97

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4. 50th prime number

Solution:

The following lists the first 50 primes
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

The following table lists the first 50 primes, with 10 columns of consecutive primes in each of the 5 rows

	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

So `50^(th)` prime number is 229

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5. 100th prime number

Solution:

The following lists the first 100 primes
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

The following table lists the first 100 primes, with 10 columns of consecutive primes in each of the 10 rows

	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

So `100^(th)` prime number is 541

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