Friday

September 4, 2015
Posted by **sarah** on Wednesday, June 24, 2009 at 2:15am.

a whole number, will produce a prime number more

than 50% of the time? Give evidence to support your

conclusion.

- math -
**MathMate**, Wednesday, June 24, 2009 at 8:42am> Do you think that

**the formula**where n is ...

Can you post**the formula**so that we can help you?

- math -
**sarah**, Wednesday, June 24, 2009 at 10:41amsorry p=6n+1 and n is a whole number

- math -
**MathMate**, Wednesday, June 24, 2009 at 11:43amAlthough the answer seems obvious, it is rather difficult to prove.

No, it is most unlikely that

p=6n+1 will yield more than 50% of primes all the time. It is true that the formula will yield more than 50% primes for n up to 147, where there are 74 primes.

The next prime occurs when n=151, and the percentage drops to 75/151<50%.

After that, the percentage decreases continually to 21% at n=1000000. In fact, there are 206345 primes of the form p=6n+1 for n <= 1000000.

Here is a list of for up to 200:

#primes/n, n:6n+1

1/1, 1:7

2/2, 2:13

3/3, 3:19

4/5, 5:31

5/6, 6:37

6/7, 7:43

7/10, 10:61

8/11, 11:67

9/12, 12:73

10/13, 13:79

11/16, 16:97

12/17, 17:103

13/18, 18:109

14/21, 21:127

15/23, 23:139

16/25, 25:151

17/26, 26:157

18/27, 27:163

19/30, 30:181

20/32, 32:193

21/33, 33:199

22/35, 35:211

23/37, 37:223

24/38, 38:229

25/40, 40:241

26/45, 45:271

27/46, 46:277

28/47, 47:283

29/51, 51:307

30/52, 52:313

31/55, 55:331

32/56, 56:337

33/58, 58:349

34/61, 61:367

35/62, 62:373

36/63, 63:379

37/66, 66:397

38/68, 68:409

39/70, 70:421

40/72, 72:433

41/73, 73:439

42/76, 76:457

43/77, 77:463

44/81, 81:487

45/83, 83:499

46/87, 87:523

47/90, 90:541

48/91, 91:547

49/95, 95:571

50/96, 96:577

51/100, 100:601

52/101, 101:607

53/102, 102:613

54/103, 103:619

55/105, 105:631

56/107, 107:643

57/110, 110:661

58/112, 112:673

59/115, 115:691

60/118, 118:709

61/121, 121:727

62/122, 122:733

63/123, 123:739

64/125, 125:751

65/126, 126:757

66/128, 128:769

67/131, 131:787

68/135, 135:811

69/137, 137:823

70/138, 138:829

71/142, 142:853

72/143, 143:859

73/146, 146:877

74/147, 147:883

75/151, 151:907

76/153, 153:919

77/156, 156:937

78/161, 161:967

79/165, 165:991

80/166, 166:997

81/168, 168:1009

82/170, 170:1021

83/172, 172:1033

84/173, 173:1039

85/175, 175:1051

86/177, 177:1063

87/178, 178:1069

88/181, 181:1087

89/182, 182:1093

90/186, 186:1117

91/187, 187:1123

92/188, 188:1129

93/192, 192:1153

94/195, 195:1171

206345/1000000, 1000000:6000001