at first , we studied in detail the solar activity behavior during the most continuous and full data set for the whole period of instrumental observations since 1610 up to 1995  the so - called group sunspot number series ( gsn , the mean yearly number values ) . three quasi - cyclic waves of increasing and decreasing the amplitude of 11  year sunspot schwabe  wolf s cycles are clear visible with a mean duration of 80100  years . their minima are well known by their labels  maunder  ( 16451715 ) ,  dalton  ( 17951830 ) , and  gleissberg ( or )  gleissberg  gnevishev  ( 18981923 ) . all these quasi - centurial waves are positioned over a general upward supercenturial trend , which starts since 1700 ad . how regular are these minimums , is there some hierarchy between them , and what is the nature of the general trend are questions of high importance for certain long term solar activity forecasts . obviously , the gsn series and even more the zurich ssn series are too short for such tasks . that is why the studies of the so - called historical series , which give indirect information for solar activity during the preinstrumental era , are of very high importance . there are two main types of  historical  data ( see   and the reference therein ) : ( a ) based on ancient or medieval manuscripts and messages for naked eye visible sunspots , aurora , bright comets , extremal climatic events , earthquakes , or other phenomena which could be related directly or indirectly to low or high solar activity ; ( b ) based on  cosmogenic  radioisotopes measurements ( mainly c and be ) . by using of different types of analysis , a main cyclic oscillation by duration of approximately 200  years in all series is detected . in context of radiocarbon data , it is popular as  de vrie s ( or swuess ) oscillation . its minimums after 1000 ad are these of oort , wolf , spoerer , maunder , and dalton in 11th , 13th , 15th , 17th , and 19th centuries , respectively . it is also clear established that maunder minimum is the deepest from all ones , followed by spoerer minimum . obviously , the period of the both minimums , that is , 15th17th centuries is the deepest phase of long term tendency , which is downward since 10001100 ad up to the maunder minimum and upward after that . it is very difficult to say something more for the nature of this trend on the base only of these tendencies . in our early study , we did a numerical time series analysis over the first version of schove s series from 1955 ad . wolf s cycle ( sc  =  11.04  years ) during the continuous part of schove s series since 296 ad . wolf s cycles magnitudes , which are pre - calculated on the base of magnitude scale by d. schove . is that the studied time series f(t ) is  scanned  by large number of simple periodic functions of type f(t ,  t )  =  a0  +  acos(2pt / t )  +  bsin(2pt / t ) by using of least squares procedure . t  is the corresponding number of time series term ( t  =  0 , 1 , 2 , n    1 ) , that is , it is related to the time . a0  is the mean value of f(t ) and p  =  3.14159 . value t0 ( usually t0  =  2 ( time series step ) ) to other chosen maximal value t max by step the last parameter could be no only equal or greater , but also essentially smaller than time series step . specifically , for our aims , we used delta t   =  1 , 0.5 , 0.25 , or 0.2 for most of our studies . for every fitting function f(t ,  t ) , the coefficient of correlation r(t )  to original series f(t ) is calculated , as well as its statistical significance is estimated . the local and statistically significant peaks of r(t ) tabulated or graphical expressed function correspond to statistically significant cycles in the studied time series . it is clearly detected that the main cyclic component is a 204  year oscillation . by less statistical significance , there are also quasi - centurial multiplets in the range of 70130  years , a 350  year cycle as well as a very long cyclic variation by duration of 11001200  years . the t r spectra of radiocarbon series during the same period as the schove s series 3rd20th centuries ( based on intcal93 radiocarbon time series , time step equal to 10  years ) are very similar . the results were obtained from time series analysis of one and the same data set  the recent part of schove s series ( since 1000 ad ) , by using of two different methods  t r periodogram analysis and method of komitov and kaftan   ( see also   and reference therein ) . the method of kaftan is a numerical technique called as the sequential analysis of dominated harmonics method . the technique was used successfully for the caspian sea level change prediction and fully described in . the bicenturial cycle is revealed as the most important for the long term solar activity kinematics during the last millennia . the bicenturial solar cycle is well detectable by using of different time series methods in all quantitative historical or instrumental time series by duration 300400  years or more . the better understanding of the nature and behavior of the supercenturial nonlinear and upward after maunder minimum trend is very important for a certain long term solar activity predictions for 21st century and beyond . the powerful quasi - bimillennial 22002400  year long , the so - called hallstadzeit cycle , is the most powerful solar activity cyclic oscillation during the postglacial epoch it is very clear shown if the super decamillenial trend ( by geomagnetic or mixed solar - geomagnetic origin ) is removed from the long term tree rings radiocarbon series . the hallstadtzeit cycle could be obtained in radiocarbon series by using of different time series analysis methods . first ideas concerning the structure of hallstadtzeit cycle are given by damon and sonett in 1991 . dergachev and chistyakov suggest such more detailed one in 1993 ( see   and the reference therein ) and recently komitov and kaftan   on the base mainly of radiocarbon intcal98 data and particularly , on the base of schove s series suggest even more detailed structure ( fig . 2 ) . according to this model , every hallstadtzeit oscillation contains two waves by duration of 11001200  years , the first one is low , and the second one is higher . the first peak is a flat , plateau - like maximum , which is relatively continuous phase by duration of 500600  years . the secondary minimum between the both quasi - millennial waves is not so deep like the starting and ending maunder - type minimums . as it is shown , the present epoch ( solar cycles from 22 to 25 ) corresponds to the transition epoch between the initial active phase and  plateau  of the present hallstadtzeit cycle . it is an important fact , which indicates that other deep maunder - type minimum is rather not possible to occur during 21st or next few centuries . an essential feature of the bicenturial cycle is their amplitude modulation by hallstadtzeit . as it is shown in fig . 3 , the amplitude of 200  year cycle is highest during the maunder - type minimums . it decreases during the upward and maximal phases and increases during the downward phases of hallstadtzeit . the last maximum , the present statement , and the expected next minimum in 21st century are shown in fig . it follows by this one that the expected in this century 200  year solar minimum should be not so deep as to spoerer one , but rather like to these of dalton or oort . r periodogram analysis  +  their extrapolation for the 21st century , has been presented in . we found that in schove s series , best expressed is the 200210-year cycle , which next minimum should be expected near to calendar year 2061 . the role of other statistical important oscillations by durations in range of 50 to 10001200  years has also taken into account in the corresponding assembled model , based on t it has been found as a result that supercenturial minimum with depth between these of dalton and oort should be occurred during the next decades . predictions for coming supercenturial minimum could be made if other long historical or instrumental time series are also used ( see   and the reference therein ) . let s consider the situation with the current sunspot solar cycle 24 and analyze its progress in the light long term solar activity dynamics . according komitov s study from 2007 , a not strong criterion for coming soon long term solar minimum is the prolongation of sunspot cycles . the  smoothed start moment  of solar cycle 24 has been determined as november 6th 2008    42  days . thus , the previous solar cycle 23 length has been about 12.4  years , and it should be classified as a long one . specifically , the very long downward phase of this cycle has been predicted successfully by kaftan and krainev in 20042005 . we found that the smoothed 24th solar cycle magnitude points ri(max )    72    27 in 2012 or 2013 . this prediction seems to be in very good agreement with the real progress of solar cycle 24 ( see http://www.swpc.noaa.gov/solarcycle/ ) . according to the presented , there predictions , which are based on historical or instrumental data sets with length in order of 300400  years or longer a supercenturial oort or dalton - type solar minimum , should be started in the first half of 21st century . but its minimal phase will probably take place in the last half of the age . the validity of long term solar activity prediction scenario is strongly related to the problem of stability and amplitude modulation of solar cycles by quasi- and bicenturial duration by the longer ones  first of all hallstadtzeit ( 22002400  year ) . solar cycle 24 should be expected to be rather moderate or even  moderate weak  , as very strong or very weak .
the solar minimum between solar cycles 23 and 24 during the period 20072009 has been the longest and deepest one at least since for the last 100  years . 
 we suggest that the sun is going to his next supercenturial minimum . 
 the main aim of this paper is to tell about arguments concerning this statement . 
 they are based on series of studies , which have been provided during the period since 1997 up to 2010 . 
 the progress of solar cycle 24 since its minimum at the end of 2008 up to the end of october 2011 in the light of long term solar activity dynamics is analyzed .