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Income taxes (Reconciliation of statutory income tax expense to provision for income taxes) (Details) - USD ($) $ in Thousands | 12 Months Ended
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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.

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- Definition Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 9 -Subparagraph (a),(b) -URI http://asc.fasb.org/extlink&oid=65882285&loc=d3e32639-109319 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08.(h)) -URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e23780-122690 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Glossary Income Tax Expense (or Benefit) -URI http://asc.fasb.org/extlink&oid=6515339 + Details
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