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Brillanti (numeri)

Rappresentazione dei numeri 

Peter Wallrodt definì “brillanti” i numeri che sono il prodotto di due primi, non necessariamente distinti, con ugual numero di cifre decimali. Includono quindi tutti i quadrati e vari semiprimi.

 

Solitamente ci si riferisce alla base 10, ma se il rapporto tra i due fattori è vicino a 1, questi avranno lo stesso numero di cifre in quasi tutte le basi, quindi un numero brillante resta tale in quasi tutte le basi.

In particolare i quadrati dei primi sono brillanti in qualsiasi base.

 

Gli unici pari sono i numeri della forma 2p, con p primo e inferiore alla base.

 

In base 10 quelli inferiori a 1000 sono: 4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781, 793, 799, 803, 817, 841, 851, 869, 871, 893, 899, 901, 913, 923, 943, 949, 961, 979, 989.

Qui trovate i numeri brillanti in base 10 sino a 107 (1.1Mbyte).

 

La tabella seguente riporta i numeri brillanti inferiori a 1000 nelle basi fino a 20.

Numero

Basi

4

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

6

2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

9

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

10

6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

14

8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

15

3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

21

3, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

22

12, 13, 14, 15, 16, 17, 18, 19, 20

25

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

26

14, 15, 16, 17, 18, 19, 20

33

12, 13, 14, 15, 16, 17, 18, 19, 20

34

18, 19, 20

35

2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

38

20

39

14, 15, 16, 17, 18, 19, 20

49

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

51

18, 19, 20

55

4, 5, 12, 13, 14, 15, 16, 17, 18, 19, 20

57

20

65

4, 5, 14, 15, 16, 17, 18, 19, 20

77

4, 5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20

85

5, 18, 19, 20

91

4, 5, 6, 7, 14, 15, 16, 17, 18, 19, 20

95

5, 20

115

5

119

5, 6, 7, 18, 19, 20

121

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

133

5, 6, 7, 20

143

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20

161

5, 6, 7

169

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

187

3, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20

203

6, 7

209

3, 5, 6, 7, 8, 9, 10, 11, 20

217

6, 7

221

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20

247

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20

253

3, 5, 6, 7, 8, 9, 10, 11

259

7

287

7

289

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

299

3, 5, 6, 7, 8, 9, 10, 11, 12, 13

301

7

319

6, 7, 8, 9, 10, 11

323

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20

329

7

341

6, 7, 8, 9, 10, 11

361

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

377

6, 7, 8, 9, 10, 11, 12, 13

391

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

403

6, 7, 8, 9, 10, 11, 12, 13

407

7, 8, 9, 10, 11

437

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

451

7, 8, 9, 10, 11

473

7, 8, 9, 10, 11

481

7, 8, 9, 10, 11, 12, 13

493

2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

517

7, 8, 9, 10, 11

527

2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

529

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

533

7, 8, 9, 10, 11, 12, 13

551

2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

559

7, 8, 9, 10, 11, 12, 13

583

8, 9, 10, 11

589

2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

611

7, 8, 9, 10, 11, 12, 13

629

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

649

8, 9, 10, 11

667

2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

671

8, 9, 10, 11

689

8, 9, 10, 11, 12, 13

697

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

703

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

713

2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

731

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

737

9, 10, 11

767

8, 9, 10, 11, 12, 13

779

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

781

9, 10, 11

793

8, 9, 10, 11, 12, 13

799

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

803

9, 10, 11

817

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

841

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

851

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

869

9, 10, 11

871

9, 10, 11, 12, 13

893

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

899

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

901

4, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

913

10, 11

923

9, 10, 11, 12, 13

943

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

949

9, 10, 11, 12, 13

961

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

979

10, 11

989

4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

 

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