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Block #163,541

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 1:49:29 AM Β· Difficulty 9.8618 Β· 6,632,597 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e5765bf4bfd98fd13268b430a7c5d5c74d758f2fc4ed80b36e9f10fb03f8a3f4
View on Chainz β†—

Height

#163,541

Difficulty

9.861764

Transactions

1

Size

198 B

Version

2

Bits

09dc9c96

Nonce

202,098

Timestamp

9/14/2013, 1:49:29 AM

Confirmations

6,632,597

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

15adf5d464fbbcf405c3df9969c21fb059de42f9b6caeac64742434a49ab0120
Transactions (1)
Coinbase15adf5d464fbbc…42434a49ab0120
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

1.069 Γ— 10⁹²(93-digit number)
10691085407425412600…04283001893013929599
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
1.069 Γ— 10⁹²(93-digit number)
10691085407425412600…04283001893013929599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.138 Γ— 10⁹²(93-digit number)
21382170814850825201…08566003786027859199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.276 Γ— 10⁹²(93-digit number)
42764341629701650402…17132007572055718399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.552 Γ— 10⁹²(93-digit number)
85528683259403300804…34264015144111436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.710 Γ— 10⁹³(94-digit number)
17105736651880660160…68528030288222873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.421 Γ— 10⁹³(94-digit number)
34211473303761320321…37056060576445747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.842 Γ— 10⁹³(94-digit number)
68422946607522640643…74112121152891494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.368 Γ— 10⁹⁴(95-digit number)
13684589321504528128…48224242305782988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.736 Γ— 10⁹⁴(95-digit number)
27369178643009056257…96448484611565977599
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:57,613,100 XPMΒ·at block #6,796,137 Β· updates every 60s
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