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Income taxes (Foreign rate differential by tax jurisdiction) (Details) - USD ($)
$ in Thousands
 12 Months Ended
Dec. 31, 2017
Dec. 31, 2016
Dec. 31, 2015
Income Tax Disclosure [Line Items]      
Pre-tax income (loss) $ 1,418,353 $ 1,433,480 $ 1,603,051
Local statutory tax rate 12.50% 12.50% 12.50%
Tax variance as a result of global activities [1] $ (13,503) $ (5,611) $ (10,462)
Permanent differences (182,481) [2] (233,084) [3] (237,352) [4]
Income from continuing operations before income tax 1,235,872 1,200,396 1,365,699
Ireland      
Income Tax Disclosure [Line Items]      
Pre-tax income (loss) $ 1,212,029 $ 1,151,387 $ 1,212,190
Local statutory tax rate [5] 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 [1] $ 0 $ 0 $ 0
United States      
Income Tax Disclosure [Line Items]      
Pre-tax income (loss) $ 72,390 $ 44,238 $ (43,825)
Local statutory tax rate [5] 35.70% 36.30% 36.30%
Variance to Irish statutory tax rate of 12.5% 23.20% 23.80% 23.80%
Tax variance as a result of global activities [1] $ 16,744 $ 10,529 $ (10,430)
The Netherlands      
Income Tax Disclosure [Line Items]      
Pre-tax income (loss) $ (61,086) $ 37,580 $ 175,897
Local statutory tax rate [5] 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 [1] $ (7,636) $ 4,698 $ 21,987
Isle of Man      
Income Tax Disclosure [Line Items]      
Pre-tax income (loss) $ 185,882 $ 181,286 $ 181,118
Local statutory tax rate [5] 0.00% 0.00% 0.00%
Variance to Irish statutory tax rate of 12.5% (12.50%) (12.50%) (12.50%)
Tax variance as a result of global activities [1] $ (23,235) $ (22,661) $ (22,640)
Other      
Income Tax Disclosure [Line Items]      
Pre-tax income (loss) $ 9,138 $ 18,989 $ 77,671
Local statutory tax rate [5] 19.30% 22.10% 13.30%
Variance to Irish statutory tax rate of 12.5% 6.80% 9.60% 0.80%
Tax variance as a result of global activities [1] $ 624 $ 1,823 $ 621
[1] The tax variance as a result of global activities is primarily caused by our operations in countries with a higher or lower statutory tax rate than the statutory tax rate in Ireland.
[2] The 2017 permanent differences included non-deductible share-based compensation in Ireland and in the Netherlands, impacts of the change in tax rate in the United States, and a valuation allowance change in respect of U.S., Dutch and Irish tax losses.
[3] The 2016 permanent differences included non-deductible share-based compensation in Ireland and in the Netherlands, non-deductible intercompany interest allocated to the United States, and a valuation allowance taken in respect of U.S., Dutch and Irish tax losses.
[4] The 2015 permanent differences included the non-deductible intercompany interest allocated to the United States, non-deductible share-based compensation in the Netherlands, non-deductible costs relating to the transfer of certain functions from the Netherlands to Ireland, and a valuation allowance taken in respect of U.S. and Dutch tax losses.
[5] The local statutory income tax expense for our significant tax jurisdictions (Ireland, the United States, the Netherlands and Isle of Man) does not differ from the actual income tax expense.