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Block #806,099

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2014, 3:13:23 AM Β· Difficulty 10.9744 Β· 6,021,036 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
6c5e6a8d8799a1ed8bfc025138ea9c105d5d49df0fe152972e7dca42a9bd10de
View on Chainz β†—

Height

#806,099

Difficulty

10.974440

Transactions

1

Size

207 B

Version

2

Bits

0af974e6

Nonce

1,833,833,854

Timestamp

11/11/2014, 3:13:23 AM

Confirmations

6,021,036

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d5c9254df1bcf96f8f7635b59bc362c68f480e885cec6d4e053993e8a75bc425
Transactions (1)
Coinbased5c9254df1bcf9…3993e8a75bc425
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.358 Γ— 10⁹⁢(97-digit number)
83581721863342343836…07826440827039569921
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
8.358 Γ— 10⁹⁢(97-digit number)
83581721863342343836…07826440827039569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.671 Γ— 10⁹⁷(98-digit number)
16716344372668468767…15652881654079139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.343 Γ— 10⁹⁷(98-digit number)
33432688745336937534…31305763308158279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.686 Γ— 10⁹⁷(98-digit number)
66865377490673875068…62611526616316559361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.337 Γ— 10⁹⁸(99-digit number)
13373075498134775013…25223053232633118721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.674 Γ— 10⁹⁸(99-digit number)
26746150996269550027…50446106465266237441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.349 Γ— 10⁹⁸(99-digit number)
53492301992539100055…00892212930532474881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.069 Γ— 10⁹⁹(100-digit number)
10698460398507820011…01784425861064949761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.139 Γ— 10⁹⁹(100-digit number)
21396920797015640022…03568851722129899521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.279 Γ— 10⁹⁹(100-digit number)
42793841594031280044…07137703444259799041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.558 Γ— 10⁹⁹(100-digit number)
85587683188062560088…14275406888519598081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,861,260 XPMΒ·at block #6,827,134 Β· updates every 60s
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