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Income taxes (Reconciliation of statutory income tax expense to provision for income taxes) (Details) - USD ($)
$ in Thousands
 12 Months Ended
Dec. 31, 2017
Dec. 31, 2016
Dec. 31, 2015
Income Tax Disclosure [Abstract]      
Statutory income tax rate 12.50% 12.50% 12.50%
Income tax expense at statutory income tax rate of 12.5% $ 154,484 $ 150,050 $ 170,712
Permanent differences 23,737 [1] 29,057 [2] 29,555 [3]
Foreign rate differential [4] (13,503) (5,611) (10,462)
Differences between statutory and actual income tax expense 10,234 23,446 19,093
Provision for income taxes $ 164,718 $ 173,496 $ 189,805
[1] 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.
[2] 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.
[3] 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.
[4] 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.