Do you think that the formula where n is
a whole number, will produce a prime number more
than 50% of the time? Give evidence to support your
conclusion.
> Do you think that the formula where n is ...
Can you post the formula so that we can help you?
sorry p=6n+1 and n is a whole number
Although 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
To determine whether the formula where n is a whole number will produce a prime number more than 50% of the time, we need to gather evidence and analyze the outcomes. Here's a step-by-step approach to find the answer:
1. Define the formula: It is essential to have a clear understanding of the formula you are referring to. Please provide the specific formula you are interested in examining.
2. Generate a sample set: To collect evidence, we need a sample set of whole numbers to apply the formula to. You can create a sample set by choosing a range of whole numbers.
3. Apply the formula: For each number in the sample set, calculate the output using the given formula.
4. Determine primality: After applying the formula to each number, examine the outputs to identify which ones are prime numbers. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself.
5. Count the number of prime outputs: Calculate the total count of prime outputs from the sample set.
6. Calculate the percentage: Divide the count of prime outputs by the total number of inputs in the sample set. Multiply the result by 100 to get the percentage of times the formula produces a prime number.
7. Analyze the percentage: If the calculated percentage is greater than 50%, it suggests that the formula tends to produce prime numbers more than half of the time. Conversely, if the percentage is lower than 50%, it implies that the formula does not generate prime numbers frequently.
To draw a conclusion supported by evidence, please provide the specific formula you want to evaluate, and we can proceed with the steps outlined above.