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Let k = 730414926864528573249. Then k*2151 + 1
is prime, k*2152 + 1 is composite,
k*2153 + 1 is prime, k*2154 + 1 is
composite, k*2155 + 1 is prime,
k*2156 + 1 is composite, k*2157 + 1
is prime, k*2158 + 1 is composite.
Unfortunately, 563 divides k*2159 + 1. [Wesolowski]
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