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

http://www.cleavebooks.co.uk/scol/calnumba.htm

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