素数新公式问题

太阳

太阳

k＝31，素数，1861位

kanyikan

特大喜讯，昌建回来了

wlc1

yangchuanju

太阳 发表于 2021-12-23 19:32
k＝31，素数，1861位

令k=3（不太合题意），有：
10^3+1=1001=7×11×13(100.00%)
10^9+1=1000000001<10>=7×11×13×19×52579(100.00%)
10^6+1-10^3=19×52579

10^93+1=100…001<94>=
7×11×13×373×44641×3590254957<10> ×909090909090909090909090909091<30>×1838190726228124463315819067778696666309&#172;1011<44>(100.00%)
10^279+1=1000000000...<280> =
7×11×13×19×373×1117×44641×52579×3590254957<10>×909090909090909090909090909091<30>×183372282864547916749018225828651<33>×18381907262281244633158190677786966663091011<44>×4887054837129490444185770642291712106451445708466643483270887621857163512076927093556902832792696796518529880218993484798134507347686651311824503<145>&#8195;(100.00%)
10^186+1-10^93=
19×1117×52579×183372282864547916749018225828651<33>×48870548371294904441857706422917121064514457084666434832708876218571635120769270&#172;9355690283279269679651852988021899348479&#172;8134507347686651311824503<145>

[10^62k+1-10^31k]/[ 10^2k+1-10^k]= [10^186+1-10^93]/[ 10^6+1-10^3]=
1117×183372…651<33>×488705…503<145>
分子中的373、44641都被消除，不能再被373、44641整除；分子不是素数。

yangchuanju

令k=5，有：
10^5+1=100001=11×9091(100.00%)
10^15+1=1000000000000001<16>=7×11×13×211×241×2161×9091(100.00%)
10^10+1-10^5=7×13×211×241×2161

10^155+1=1000000000...<156>=
11×9091×11161×3925963357681<13>×5167617497664851<16>×909090909090909090909090909091<30>×4857900688365130469291831549890842547443&#172;9173769354062250546461438565798929702369&#172;11030721<88>(100.00%)

10^465+1=1000000000...<466>=
7×11×13×211×241×373×2161×9091×11161×44641×3590254957<10>×3925963357681<13>×5167617497664851<16>×22672589441232691<17>×909090909090909090909090909091<30>×6548241632713397411808073416931<31>×553114664478262993662992814601370587114291<42>×18381907262281244633158190677786966663091011<44>×3093888678771257769541252942946202755752229401<46>×1158334526259936604206939942487445760921582415411<49>×3092189186638711651761630213691413266133197806226014052371<58>×4857900688365130469291831549890842547443917376935406225054646143856579892970236911030721<88>(100.00%)

10^310+1-10^155=
7×13×211×241×373×2161×44641×3590254957<10>×22672589441232691<17>×6548241632713397411808073416931<31>×553114664478262993662992814601370587114291<42>×18381907262281244633158190677786966663091011<44>×3093888678771257769541252942946202755752229401<46>×1158334526259936604206939942487445760921582415411<49>×3092189186638711651761630213691413266133197806226014052371<58>

[10^62k+1-10^31k]/[ 10^2k+1-10^k]= [10^310+1-10^155]/[ 10^10+1-10^6]=
373×44641×3590254957<10>×22672589441232691<17>×6548241632713397411808073416931<31>×553114664478262993662992814601370587114291<42>×18381907262281244633158190677786966663091011<44>×3093888678771257769541252942946202755752229401<46>×1158334526259936604206939942487445760921582415411<49>×3092189186638711651761630213691413266133197806226014052371<58>
分子中的373、44641都被保留，能被373、44641整除；分子不是素数。

yangchuanju

令k=31，有：
10^31+1=1000…001<32>=
11×909090909090909090909090909091<30>(100.00%)
10^93+1=1000…001<94>=
7×11×13×373×44641×3590254957<10>×909090909090909090909090909091<30>×1838190726228124463315819067778696666309&#172;1011<44>(100.00%)
10^62+1-10^31=
7×13×373×44641×3590254957<10>×1838190726228124463315819067778696666309&#172;1011<44>

10^961+1=1000000000...<962>=
11×17299×909090909090909090909090909091<30>×[5780680964...<926>](3.67%)
10^2883+1=1000000000...<2884>=
7×11×13×373×17299×44641×3590254957<10>×32471355853<11>×93087297464503<14>×909090909090909090909090909091<30>×104274315198051542548629408277973929<36>×18381907262281244633158190677786966663091011<44>×[5780680964...<926>]×[3172720454...<1801>](5.44%)
10^1922+1-10^961=
7×13×373×44641×3590254957<10>×32471355853<11>×93087297464503<14>×104274315198051542548629408277973929<36>×18381907262281244633158190677786966663091011<44>×[3172720454...<1801>]

[10^62k+1-10^31k]/[ 10^2k+1-10^k]= [10^1922+1-10^961]/[ 10^62+1-10^31]=
32471355853<11>×93087297464503<14>×104274315198051542548629408277973929<36>×[3172720454...<1801>]
同素数3，分子中的373、44641都被消除，不能再被373、44641整除；分子不是素数。

yangchuanju

令k=31，有：
10^31+1=1000…001<32>=
11×909090909090909090909090909091<30>(100.00%)
10^93+1=1000…001<94>=
7×11×13×373×44641×3590254957<10>×909090909090909090909090909091<30>×1838190726228124463315819067778696666309&#172;1011<44>(100.00%)
10^62+1-10^31=
7×13×373×44641×3590254957<10>×1838190726228124463315819067778696666309&#172;1011<44>

10^961+1=1000000000...<962>=
11×17299×909090909090909090909090909091<30>×[5780680964...<926>](3.67%)
10^2883+1=1000000000...<2884>=
7×11×13×373×17299×44641×3590254957<10>×32471355853<11>×93087297464503<14>×909090909090909090909090909091<30>×104274315198051542548629408277973929<36>×18381907262281244633158190677786966663091011<44>×[5780680964...<926>]×[3172720454...<1801>](5.44%)
10^1922+1-10^961=
7×13×373×44641×3590254957<10>×32471355853<11>×93087297464503<14>×104274315198051542548629408277973929<36>×18381907262281244633158190677786966663091011<44>×[3172720454...<1801>]

[10^62k+1-10^31k]/[ 10^2k+1-10^k]= [10^1922+1-10^961]/[ 10^62+1-10^31]=
32471355853<11>×93087297464503<14>×104274315198051542548629408277973929<36>×[3172720454...<1801>]
同素数3，分子中的373、44641都被消除，不能再被373、44641整除；分子不是素数。

yangchuanju

太阳先生此题的宗旨是什么？
太阳先生究竟想说明什么？是要网友证明，还是你证明？

是要证明分子只要不能被373和44641整除，分子就一定是素数吗？
素数31大于3，分子不能被373、44641整除，分子不是素数呀！
2楼太阳先生的k=31，多少多少位，什么意思？

还是要寻找分子不能被373和44641整除，且分子是素数的k？
尚若如此，请把“求证”改为“请搜寻…是素数的k”。

wlc1