In the first decade of numbers (1-10), there are four prime numbers (2,3,5,7). In the second decade (11-20), there are another four (11,13,17,19).
Are there other such decades with four prime numbers?
(In reply to
spoiler by Robby Goetschalckx)
101 103 107 109
191 193 197 199
821 823 827 829
1481 1483 1487 1489
1871 1873 1877 1879
2081 2083 2087 2089
3251 3253 3257 3259
3461 3463 3467 3469
5651 5653 5657 5659
9431 9433 9437 9439
13001 13003 13007 13009
15641 15643 15647 15649
15731 15733 15737 15739
16061 16063 16067 16069
18041 18043 18047 18049
18911 18913 18917 18919
19421 19423 19427 19429
21011 21013 21017 21019
22271 22273 22277 22279
25301 25303 25307 25309
31721 31723 31727 31729
34841 34843 34847 34849
43781 43783 43787 43789
51341 51343 51347 51349
55331 55333 55337 55339
62981 62983 62987 62989
67211 67213 67217 67219
69491 69493 69497 69499
72221 72223 72227 72229
77261 77263 77267 77269
79691 79693 79697 79699
81041 81043 81047 81049
82721 82723 82727 82729
88811 88813 88817 88819
97841 97843 97847 97849
99131 99133 99137 99139
101111 101113 101117 101119
109841 109843 109847 109849
116531 116533 116537 116539
119291 119293 119297 119299
122201 122203 122207 122209
135461 135463 135467 135469
144161 144163 144167 144169
157271 157273 157277 157279
165701 165703 165707 165709
166841 166843 166847 166849
10 N1=11:N2=13:N3=17:N4=19
15 while 1=1
20 N5=nxtprm(N4)
30 N1=N2:N2=N3:N3=N4:N4=N5
40 if N4-N1<10 then print N1,N2,N3,N4:Ct=Ct+1
45 if Ct>45 then end
50 wend
This program did not specifically require that the first of the four primes in each group must end in a digit 1, but they do. So you can see that such groups are possible only with the first of them ending in a digit 1, and the others, in turn, must end in 3, 7 and 9. Inclusion of a number ending in 5 is impossible, as such a number would be divisible by 5, and not be prime (outside the first decade). A sequence such as ...3, ...7, ...9, ...1, in that order, would also be impossible, as one of the last three has to be divisible by 3. Similarly for ...7, ...9, ...1, ...3 and ...9, ...1, ...3, ...7.
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Posted by Charlie
on 2006-11-06 09:13:22 |
re: spoiler -- more
