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Income taxes (Foreign rate differential by tax jurisdiction) (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Income Tax Disclosure [Line Items]
Pre-tax income (loss)	$ 1,333,046	$ 1,158,620	$ 1,418,353
Local statutory tax rate	12.50%	12.50%	12.50%
Tax variance as a result of global activities	$ 1,083	$ (803)	$ (13,503)
Permanent differences	7,596	(7,687)	(182,481)
Income from continuing operations before income tax	1,340,642	1,150,933	1,235,872
Ireland
Income Tax Disclosure [Line Items]
Pre-tax income (loss)	$ 1,324,100	$ 1,163,574	$ 1,212,029
Local statutory tax rate	12.50%	12.50%	12.50%
Variance to Irish statutory tax rate of 12.5%	0.00%	0.00%	0.00%
Tax variance as a result of global activities	$ 0	$ 0	$ 0
United States
Income Tax Disclosure [Line Items]
Pre-tax income (loss)	$ (30,041)	$ (85)	$ 72,390
Local statutory tax rate	21.00%	22.00%	35.70%
Variance to Irish statutory tax rate of 12.5%	8.50%	9.50%	23.20%
Tax variance as a result of global activities	$ (2,553)	$ (8)	$ 16,744
The Netherlands
Income Tax Disclosure [Line Items]
Pre-tax income (loss)	$ 30,656	$ 6,108	$ (61,086)
Local statutory tax rate	25.00%	25.00%	25.00%
Variance to Irish statutory tax rate of 12.5%	12.50%	12.50%	12.50%
Tax variance as a result of global activities	$ 3,832	$ 764	$ (7,636)
Isle of Man
Income Tax Disclosure [Line Items]
Pre-tax income (loss)			$ 185,882
Local statutory tax rate			0.00%
Variance to Irish statutory tax rate of 12.5%			(12.50%)
Tax variance as a result of global activities			$ (23,235)
Other
Income Tax Disclosure [Line Items]
Pre-tax income (loss)	$ 8,331	$ (10,977)	$ 9,138
Local statutory tax rate	10.10%	26.70%	19.30%
Variance to Irish statutory tax rate of 12.5%	(2.40%)	14.20%	6.80%
Tax variance as a result of global activities	$ (196)	$ (1,559)	$ 624

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Income (loss) from continuing operations before equity method investments, income taxes, extraordinary items, noncontrolling interest, non taxable income

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Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

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