Abstract
For any positive integer [Formula: see text], we exhibit a prime knot [Formula: see text] with [Formula: see text] crossings whose Jones polynomial [Formula: see text] is equal to [Formula: see text] modulo [Formula: see text]. Our construction rests on a certain [Formula: see text]-crossing prime tangle [Formula: see text] which is undetectable by the Kauffman bracket polynomial pair mod [Formula: see text].
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