table of primes between the first 100 squares

table of primes between the first 100 squares

In support of Legendre’s

conjecture

, the following table lists the first

hundred

square numbers

and the

prime numbers

that are between them. (Of course a single

counterexample

is enough to disprove).

n

2

(

n

+

1

)

2

n

2

<

p

<

(

n

+

1

)

2

1

4

2, 3

4

9

5, 7

9

16

11, 13

16

25

17, 19, 23

25

36

29, 31

36

49

37, 41, 43, 47

49

64

53, 59, 61

64

81

67, 71, 73, 79

81

100

83, 89, 97

100

121

101, 103, 107, 109, 113

121

144

127, 131, 137, 139

144

169

149, 151, 157, 163, 167

169

196

173, 179, 181, 191, 193

196

225

197, 199, 211, 223

225

256

227, 229, 233, 239, 241, 251

256

289

257, 263, 269, 271, 277, 281, 283

289

324

293, 307, 311, 313, 317

324

361

331, 337, 347, 349, 353, 359

361

400

367, 373, 379, 383, 389, 397

400

441

401, 409, 419, 421, 431, 433, 439

441

484

443, 449, 457, 461, 463, 467, 479

484

529

487, 491, 499, 503, 509, 521, 523

529

576

541, 547, 557, 563, 569, 571

576

625

577, 587, 593, 599, 601, 607, 613, 617, 619

625

676

631, 641, 643, 647, 653, 659, 661, 673

676

729

677, 683, 691, 701, 709, 719, 727

729

784

733, 739, 743, 751, 757, 761, 769, 773

784

841

787, 797, 809, 811, 821, 823, 827, 829, 839

841

900

853, 857, 859, 863, 877, 881, 883, 887

900

961

907, 911, 919, 929, 937, 941, 947, 953

961

1024

967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021

1024

1089

1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087

1089

1156

1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153

1156

1225

1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223

1225

1296

1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291

1296

1369

1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367

1369

1444

1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439

1444

1521

1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511

1521

1600

1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597

1600

1681

1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669

1681

1764

1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759

1764

1849

1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847

1849

1936

1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933

1936

2025

1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017

2025

2116

2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113

2116

2209

2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207

2209

2304

2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297

2304

2401

2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399

2401

2500

2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477

2500

2601

2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593

2601

2704

2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699

2704

2809

2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803

2809

2916

2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909

2916

3025

2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023

3025

3136

3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121

3136

3249

3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229

3249

3364

3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361

3364

3481

3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469

3481

3600

3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593

3600

3721

3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719

3721

3844

3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833

3844

3969

3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967

3969

4096

3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093

4096

4225

4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219

4225

4356

4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349

4356

4489

4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483

4489

4624

4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621

4624

4761

4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759

4761

4900

4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889

4900

5041

4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039

5041

5184

5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179

5184

5329

5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323

5329

5476

5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471

5476

5625

5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623

5625

5776

5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749

5776

5929

5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927

5929

6084

5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079

6084

6241

6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229

6241

6400

6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397

6400

6561

6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553

6561

6724

6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719

6724

6889

6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883

6889

7056

6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043

7056

7225

7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219

7225

7396

7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393

7396

7569

7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561

7569

7744

7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741

7744

7921

7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919

7921

8100

7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093

8100

8281

8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273

8281

8464

8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461

8464

8649

8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647

8649

8836

8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831

8836

9025

8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013

9025

9216

9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209

9216

9409

9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403

9409

9604

9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601

9604

9801

9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791

9801

10000

9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973

10000

10201

10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193

Title

table of primes between the first 100 squares

Canonical

name

TableOfPrimesBetweenTheFirst100Squares

Date of creation

2013-03-22 16:38:20

Last modified on

2013-03-22 16:38:20

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Example

Classification

msc 11A41

Generated on Fri Feb 9 15:18:45 2018 by

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