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Block #205,511

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/12/2013, 4:57:38 AM Β· Difficulty 9.9000 Β· 6,621,892 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9bb779acd01f162219d4ca63263eba6f2b6da43948987cede6f43574bafb1d6
View on Chainz β†—

Height

#205,511

Difficulty

9.899991

Transactions

1

Size

198 B

Version

2

Bits

09e665d5

Nonce

231,828

Timestamp

10/12/2013, 4:57:38 AM

Confirmations

6,621,892

Mined by

⛏️ P2SHAbJUC2oSrZY84nuu7WUoHPgJjAcpKam6LK

Merkle Root

3fc444ff2077370e80246fcbba084f03259edd3c9eabc268d088dade128f0f91
Transactions (1)
Coinbase3fc444ff207737…88dade128f0f91
1 in β†’ 1 out10.1900 XPM109 B
AbJUC2oS…cpKam6LK
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.

3.052 Γ— 10⁹³(94-digit number)
30520782350124482807…80390559207822415709
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.052 Γ— 10⁹³(94-digit number)
30520782350124482807…80390559207822415709
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.104 Γ— 10⁹³(94-digit number)
61041564700248965614…60781118415644831419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁴(95-digit number)
12208312940049793122…21562236831289662839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.441 Γ— 10⁹⁴(95-digit number)
24416625880099586245…43124473662579325679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.883 Γ— 10⁹⁴(95-digit number)
48833251760199172491…86248947325158651359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.766 Γ— 10⁹⁴(95-digit number)
97666503520398344982…72497894650317302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.953 Γ— 10⁹⁡(96-digit number)
19533300704079668996…44995789300634605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.906 Γ— 10⁹⁡(96-digit number)
39066601408159337993…89991578601269210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.813 Γ— 10⁹⁡(96-digit number)
78133202816318675986…79983157202538421759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
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