Keep discovering.

This is a short path through every one of Discover Alone's real place records. Follow the first choice each time to move through the complete archive, or take another branch.

The archive in numbers

Lemma 1 · Complete cycle

pₙ₊₁ = (pₙ + 1) mod 237,537

Adding one has no common divisor with the archive size except one. The first choice therefore reaches every one of the 237,537 place pages exactly once before it repeats.

Lemma 2 · Six ways onward

D = {1, 97, 997, 10,007, 50,021, 100,003}

Each page offers these six forward distances. The distance of one preserves the complete cycle; the other five jump to far-apart parts of the same archive.

Lemma 3 · County total

Σ Ncounty = 237,606; unique pages = 237,537

The 32 county lists contain 237,606 placements. They become 237,537 different page addresses because 69 placements repeat an address already present in another county list.

All 32 county counts
Antrim6,564
Armagh1,424
Carlow2,399
Cavan4,271
Clare10,203
Cork29,379
Derry2,605
Donegal6,950
Down5,464
Dublin12,718
Fermanagh3,131
Galway15,690
Kerry16,101
Kildare5,055
Kilkenny8,382
Laois3,254
Leitrim2,929
Limerick10,994
Longford3,609
Louth3,980
Mayo11,356
Meath6,546
Monaghan3,057
Offaly6,327
Roscommon7,241
Sligo7,877
Tipperary12,011
Tyrone2,717
Waterford6,511
Westmeath6,399
Wexford7,526
Wicklow4,936

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