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Block #112,867

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/12/2013, 5:30:42 AM Β· Difficulty 9.7265 Β· 6,704,491 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a7a2a3e51cb776903289169c094fde9cd6de8cc47dae04b9d728e14fde8b93f9
View on Chainz β†—

Height

#112,867

Difficulty

9.726457

Transactions

1

Size

198 B

Version

2

Bits

09b9f910

Nonce

25,679

Timestamp

8/12/2013, 5:30:42 AM

Confirmations

6,704,491

Mined by

⛏️ P2SHAKErQXMSbzQTkoT3CyUmWJvi8LJWgaCTzm

Merkle Root

68efd0feb74cf3a19b6f15fb812a5e13a57095e875e4c164369b2b0b45722ead
Transactions (1)
Coinbase68efd0feb74cf3…9b2b0b45722ead
1 in β†’ 1 out10.5500 XPM109 B
AKErQXMS…JWgaCTzm
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.

7.425 Γ— 10⁹²(93-digit number)
74259613444070332254…31874400660433191681
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
7.425 Γ— 10⁹²(93-digit number)
74259613444070332254…31874400660433191681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.485 Γ— 10⁹³(94-digit number)
14851922688814066450…63748801320866383361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.970 Γ— 10⁹³(94-digit number)
29703845377628132901…27497602641732766721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.940 Γ— 10⁹³(94-digit number)
59407690755256265803…54995205283465533441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.188 Γ— 10⁹⁴(95-digit number)
11881538151051253160…09990410566931066881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.376 Γ— 10⁹⁴(95-digit number)
23763076302102506321…19980821133862133761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.752 Γ— 10⁹⁴(95-digit number)
47526152604205012643…39961642267724267521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.505 Γ— 10⁹⁴(95-digit number)
95052305208410025286…79923284535448535041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.901 Γ— 10⁹⁡(96-digit number)
19010461041682005057…59846569070897070081
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 Second 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 2CC formula:

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