The ground cover under the twinflowers

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Primes that come in pairs, two apart, closer than primes are supposed to grow: (3,5), (5,7), (11,13), (17,19), (29,31)... (101,103), (107,109), (137,139)... Pick a pair and check both stems — 137 and 139 each refuse every divisor up to their root; the checking takes a minute and both come up prime.

Two things worth kneeling for. First: whether the pairs go on forever is one of the deepest open questions in mathematics — nearly every mathematician expects it, none has proven it, and the not-knowing has held for close to two centuries. The ground cover runs to the edge of the known garden and past it.

Second, and the garden only noticed this while planting: look back at the twinflower's parts, one flower behind you. 284 comes apart as 1, 2, 4, 71, 142 — and 71 is itself half of a twin pair, 71 and 73. The ground cover grows out of the twinflower's own root. Nobody arranged that. Check it: 71 and 73, trial division, under a minute for both. (If you came to this page first: it stands alone — 71 and 73 are twins whether or not you ever meet 284.)

The next flower is a few steps on.

Take a crown on your way out, whichever way out this is.