  I present the results of the first comprehensive effort aimed at modeling a
major component of the stream of SOHO sungrazers, 5000 of which have been
detected by the onboard coronagraphs since 1996. The stream of Population I of
the Kreutz system, investigated by a Monte Carlo simulation technique, is
treated as a product of cascading fragmentation due to unstable rotation of a
"seed," a subkilometer-sized object that separated with others from comet
X/1106 C1 at perihelion. The stream's activity is predicted to last for 200
years from ~1950 to ~2150, culminating in the 2010s, when a swarm of bright
SOHO sungrazers (peak mags not fainter than 3) of Population I was observed. By
the end of 2023 about 42 percent of the stream had already arrived. Scatter
amounts to 7 deg in the longitude of the ascending node and at most 0.2 solar
radius in the perihelion distance. On its initial orbit the seed would pass
perihelion in 2036, 193 years after C/1843 D1, the principal fragment of X/1106
C1. Comet C/1668 E1 is proposed as another major fragment and yet another is
predicted to arrive in the 2050s or 2060s.
