## Tuesday, November 23, 2010

### Finding Prime Numbers in Binary such as

How many primes among the positive integers, written as usual in base 10, are alternating 1’s and 0’s, beginning and ending with 1?

Tools:
The Number Base Calculator

`The First 10,000 Primes`
`http://primes.utm.edu/lists/small/10000.txt`

Base 10 .................................... Base 2

2 ................................................. 10
3 ................................................. 11
5 ................................................. 101 (Yes)
7 ................................................. 111
11 ................................................ 1011
13 ................................................ 1101
17 ................................................ 10001 (the 0's and 1's do not alternate)
19 ................................................ 10011
23 ................................................ 10111
29 ................................................ 11101
31 ................................................ 11111
37 ................................................ 100101 (not quite)
41 ................................................ 101001 (not quite)
43 ................................................ 101011
47 ................................................ 101111
53 ................................................ 110101
59 ................................................ 111011
61 ................................................ 111101
67 ................................................ 1000011
71 ................................................ 1000111
73
79
83
89
97
101
103
107
109
113
127
131
137
139
149
151
157
163
167
173
179
181
191
193
197
199
211
223
227
229
233
239
241
251
257
263
269
271
277
281