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Block #207,857

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 4:31:25 PM Β· Difficulty 9.9042 Β· 6,598,233 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
97d76fcf2d3e9d9de7ad1bd08779fa8710ccecc0282359c410101405db482845
View on Chainz β†—

Height

#207,857

Difficulty

9.904227

Transactions

1

Size

198 B

Version

2

Bits

09e77b69

Nonce

11,935

Timestamp

10/13/2013, 4:31:25 PM

Confirmations

6,598,233

Mined by

⛏️ P2SHAGD4ELPmV9VxECkLLRQiFxvMNQsYtybN6f

Merkle Root

0ff21879ab4844ab6c7b62c5deb6215fd9ae55ed8dbb31b6eff66fa149faa8ef
Transactions (1)
Coinbase0ff21879ab4844…f66fa149faa8ef
1 in β†’ 1 out10.1800 XPM109 B
AGD4ELPm…sYtybN6f
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.

1.439 Γ— 10⁹³(94-digit number)
14394905252910864652…96833219479696087039
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
1.439 Γ— 10⁹³(94-digit number)
14394905252910864652…96833219479696087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.878 Γ— 10⁹³(94-digit number)
28789810505821729305…93666438959392174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.757 Γ— 10⁹³(94-digit number)
57579621011643458611…87332877918784348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.151 Γ— 10⁹⁴(95-digit number)
11515924202328691722…74665755837568696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.303 Γ— 10⁹⁴(95-digit number)
23031848404657383444…49331511675137392639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.606 Γ— 10⁹⁴(95-digit number)
46063696809314766889…98663023350274785279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.212 Γ— 10⁹⁴(95-digit number)
92127393618629533779…97326046700549570559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.842 Γ— 10⁹⁡(96-digit number)
18425478723725906755…94652093401099141119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.685 Γ— 10⁹⁡(96-digit number)
36850957447451813511…89304186802198282239
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:57,692,792 XPMΒ·at block #6,806,089 Β· updates every 60s
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