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math

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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.

  • math - ,

    > Do you think that the formula where n is ...

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

  • math - ,

    sorry p=6n+1 and n is a whole number

  • math - ,

    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

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