For n=4, test square spirals centered at each positive integer until one is found which lies in a 4 X 4 square of nonprimes. Square spirals centered at 1..132 do not work, then for 133 the following square spiral is produced:
.
197 196 195 194 193 192 191 190 189
.
198 169 168 167 166 165 164 163 188
. +------------------+
199 170 149 148 |147 146 145 162| 187
. | |
200 171 150 137 |136 135 144 161| 186
. | |
201 172 151 138 |133 134 143 160| 185
. | |
202 173 152 139 |140 141 142 159| 184
. +------------------+
203 174 153 154 155 156 157 158 183
.
204 175 176 177 178 179 180 181 182
.
205 206 207 208 209 210 211 212 213
.
Note that 147, 146, 145, 162, 136, 135, 144, 161, 133, 134, 143, 160, 140, 141, 142, and 159 are all nonprime, so the square spiral centered at 133 works.
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