I just tried to do a Google search to discover what calendrical reckoning you use to get the date '7/4/1826,' but I came up blank.
2005-February-13 corresponds to 5765-Adar Aleph-04 in the Hebrew calendar, 2005-January-31 in the Julian calendar, 1426-Muharram-04 in the Islamic calendar, 1721-Amshir-06 in the Coptic calendar, 1997-Yakatit-6 in the Ethiopic calendar, 0161-Mulk-07 in the Bahai calendar, 1926-Magha-24 in the Indian civil calendar and 1383-Bahman-25 in the Persian calendar. But none of those correspond to 1826-07-04.
Sorry. I thought certain things were common knowledge.
On July 4, 1826, the 50th anniversary of the Declaration of Independence, Thomas Jefferson and John Adams, the two men most responsible for same, died within hours of each other. Jefferson's last words, "Is it the 4th?" And Adams, "Jefferson lives", which was technically wrong, but that was before email. The whole nation was stunned by the "coincidence" and it was widely viewed as a sign of the blessing of God on our still young country.