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Block #125,716

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/20/2013, 10:43:34 AM Β· Difficulty 9.7771 Β· 6,684,628 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2cf8da3adde29cf718b00f79620adf5e8cff449c38b5ba95cd14dbad5676738e
View on Chainz β†—

Height

#125,716

Difficulty

9.777098

Transactions

1

Size

200 B

Version

2

Bits

09c6efe0

Nonce

340,401

Timestamp

8/20/2013, 10:43:34 AM

Confirmations

6,684,628

Mined by

⛏️ P2SHASqD45bJV3sZxYheFf4Fkcm7gpvaReDTwF

Merkle Root

39b7b37c815e7538c7782a650cf1933ddc0480995df88898d4a28a59fe0f45a5
Transactions (1)
Coinbase39b7b37c815e75…a28a59fe0f45a5
1 in β†’ 1 out10.4500 XPM109 B
ASqD45bJ…vaReDTwF
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.

4.861 Γ— 10⁹⁢(97-digit number)
48613331561198321010…94691625418398010879
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
4.861 Γ— 10⁹⁢(97-digit number)
48613331561198321010…94691625418398010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.722 Γ— 10⁹⁢(97-digit number)
97226663122396642021…89383250836796021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁷(98-digit number)
19445332624479328404…78766501673592043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.889 Γ— 10⁹⁷(98-digit number)
38890665248958656808…57533003347184087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.778 Γ— 10⁹⁷(98-digit number)
77781330497917313617…15066006694368174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.555 Γ— 10⁹⁸(99-digit number)
15556266099583462723…30132013388736348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.111 Γ— 10⁹⁸(99-digit number)
31112532199166925446…60264026777472696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.222 Γ— 10⁹⁸(99-digit number)
62225064398333850893…20528053554945392639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.244 Γ— 10⁹⁹(100-digit number)
12445012879666770178…41056107109890785279
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:57,726,834 XPMΒ·at block #6,810,343 Β· updates every 60s
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