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Published 01/10/24
pràdhainn f. [ˈpʰɾaː-iɲ]. Citing Greene (1978, 121), McDonald (2009, 345) considers SG pràdhainn and [Ir.] práidhinn to be likely loans from ON bráðung f. ‘haste’.
The derivation is first suggested by O’Rahilly 1942c, 200, a fact acknowledged by Greene (1976, 80), who is cited by Ó Muirithe 2010, s.v. (Ir.) práidhinn, práinn.
Among a group of nouns that for the sake of convenience he calls ‘necessary loans’ (along with half a dozen verbs of general meaning), Greene notes that the Old Norse loan práidhinn ‘press of business, distress’ as an abstract noun is ‘conspicuous by its isolation’. Dinneen (1947) gives Ir. práidhinn f. ‘urgency, a difficulty, need; trepidaton, hurry, flurry, rush; regard, heed, pride, delight’, alias prádhainn and práinn, and the adjectival forms práidhneach, práidhinneach, práinneach, while Ó Dónaill (1977) cites práinn f., alias práidhinn, and the adjectival forms práinneach and práidhinneach; the latter also gives separate entries for ‘hurry, rush, urgent need, exigency’ on the one hand and ‘liking, fondness, pride, delight’ on the other. Práinn occurs for example in Co. Waterford (Ó hAirt 1988) and Galway (Ó Curnáin 2007 I, 529), práidhinn for example in Donegal (Quiggin 1906, 72: [práidhinneach]) and Rathlin (Holmer 1942, 224), the latter corresponding with disyllabic forms from Scotland: 
For a more detailed account of the situation in Irish, see O’Rahilly 1942c.
praidhin ‘earnest business, great haste’ and praidhinach [adj.] (Shaw 1780); praidhinn f. ‘ditto; flurry’ and praidhinneach adj. (citing Shaw), and praidhinneachd f. (Armstrong 1925); praidhean f. ‘ditto’ (citing Shaw and O’Reilly 1864), praidhinn f. ‘affliction’ and praidhinneach adj. (HSS 1828); pradhainn [prā´ėnn] f. ‘press of business, throng, throngness’ (McAlpine 1832); while pràidhinn f. /praːjɪNʲ/ and pràdhainn f. /praː.ɪNʲ/ ‘haste, hurry; urgency; pride’ are listed separately in AFB˄.
Noting the latter occurs in South Uist.
While a derivation of these forms from ON bráðung f. (a derivative of bráðr adj. ‘hasty’) is just possible phonetically given a number of assumptions, 
O’Rahilly 1942c, 200. O’Rahilly 1976, 242, simply notes that Ir. práinn has developed from práidhinn.
MacBain’s (1911) derivation from OG brothaḋ m. ‘short period of time, moment’ seems improbable. Perhaps a more likely source for the range of Irish and Scottish Gaelic forms both phonetically and semantically, however, is MScots brayn(e), brane (Scots ‡brain) adj. ‘furious’ and MEng. (north-west midlands) brayn adj. ‘furious, mad’, possibly truncated forms of MEng. brayn-wode, 
The earliest instance in Irish literature is a 16th-century example in a poem by Giolla-na-naomh Ruadh Mac Eochadha: ó thárla a bpraidhinn tinnis (Book of O’Byrnes (Harvard MS) f.30.a.11, cited in O’Rahilly 1942c, 198). For Scottish Gaelic, DASG˄ lists an instance in the sense ?‘pressure of business’ (Mac-Talla II, No. 3, p. 7 (1893): Mura d’thig pradhainn teann orm cluinnidh sibh uam fathast an uinne ghoirid) and one in the sense, according to its editor (p. 8), ‘press of business, throngness’ (Sinclair 1900, 5: Nam bu ni e ’bhiodh òrdaichte | Do mhac òg a bhith t’ àite, | ’Chumail pràdhainn ’san teaghlach | Ann an siud mar a tha e).
lit. ‘brain-mad’ (SND˄, DOST˄, OED˄): MScots brayn(e), brane and MEng. brayn might well account for both monosyllabic and disyllabic forms above, as well as the semantic developments ‘mad (furious)’ → ‘rush; pressure’ on the one hand and ‘mad (obsessive)’ → ‘delight, pride; affliction’ on the other.