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Block #77,377

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2013, 9:43:51 AM Β· Difficulty 9.1664 Β· 6,718,018 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd9c62b3625cb806af92b2f0016246cd2ced3d884f0245e51ecdff742c32b585
View on Chainz β†—

Height

#77,377

Difficulty

9.166369

Transactions

1

Size

199 B

Version

2

Bits

092a9730

Nonce

332

Timestamp

7/22/2013, 9:43:51 AM

Confirmations

6,718,018

Mined by

⛏️ P2SHAPBKnjMC5rxCJr1YqYG11mgYuibfkPQ8AB

Merkle Root

6712d2116306707a5a16970553acfba80df732dc525ad5b95cc7a93b74563b90
Transactions (1)
Coinbase6712d211630670…c7a93b74563b90
1 in β†’ 1 out11.8800 XPM110 B
APBKnjMC…bfkPQ8AB
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.

1.491 Γ— 10⁹²(93-digit number)
14917785155036797926…89667292827326738001
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
1.491 Γ— 10⁹²(93-digit number)
14917785155036797926…89667292827326738001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.983 Γ— 10⁹²(93-digit number)
29835570310073595852…79334585654653476001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.967 Γ— 10⁹²(93-digit number)
59671140620147191704…58669171309306952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.193 Γ— 10⁹³(94-digit number)
11934228124029438340…17338342618613904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.386 Γ— 10⁹³(94-digit number)
23868456248058876681…34676685237227808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.773 Γ— 10⁹³(94-digit number)
47736912496117753363…69353370474455616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.547 Γ— 10⁹³(94-digit number)
95473824992235506726…38706740948911232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.909 Γ— 10⁹⁴(95-digit number)
19094764998447101345…77413481897822464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.818 Γ— 10⁹⁴(95-digit number)
38189529996894202690…54826963795644928001
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
Circulating Supply:57,607,219 XPMΒ·at block #6,795,394 Β· updates every 60s
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