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Block #204,604

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/11/2013, 2:47:57 PM Β· Difficulty 9.8988 Β· 6,590,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
266515f38b932c03b86f7b7b428e9c64403a2fc9ab0851fbf81b2f020b360d4b
View on Chainz β†—

Height

#204,604

Difficulty

9.898790

Transactions

2

Size

1016 B

Version

2

Bits

09e6171d

Nonce

4,504

Timestamp

10/11/2013, 2:47:57 PM

Confirmations

6,590,186

Mined by

⛏️ P2SHAWT4FajAqvKnh9YhmpgjgT5GAa7qUxCsaJ

Merkle Root

02c481b3a88aebbe288b777e599904e3e46799a9ef3492933bf8ec1b6873372b
Transactions (2)
Coinbase70027522ea52d1…460beac156018f
1 in β†’ 1 out10.2000 XPM109 B
AWT4FajA…7qUxCsaJ
13a326675f5026…a98ead4d63a42c
5 in β†’ 2 out30.0686 XPM817 B
AZoTowvW…KJoS4PJAAYu85K2j…5L7AsmQc
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.

2.123 Γ— 10⁹⁡(96-digit number)
21233179546342329117…13603361420070282399
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
2.123 Γ— 10⁹⁡(96-digit number)
21233179546342329117…13603361420070282399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.246 Γ— 10⁹⁡(96-digit number)
42466359092684658235…27206722840140564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.493 Γ— 10⁹⁡(96-digit number)
84932718185369316470…54413445680281129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.698 Γ— 10⁹⁢(97-digit number)
16986543637073863294…08826891360562259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.397 Γ— 10⁹⁢(97-digit number)
33973087274147726588…17653782721124518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.794 Γ— 10⁹⁢(97-digit number)
67946174548295453176…35307565442249036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.358 Γ— 10⁹⁷(98-digit number)
13589234909659090635…70615130884498073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.717 Γ— 10⁹⁷(98-digit number)
27178469819318181270…41230261768996147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.435 Γ— 10⁹⁷(98-digit number)
54356939638636362540…82460523537992294399
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
Circulating Supply:57,602,373 XPMΒ·at block #6,794,789 Β· updates every 60s
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