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Block #29,818

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 4:50:43 PM Β· Difficulty 7.9855 Β· 6,766,742 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
816de112fa00372bd3912b0f47714109d0a29c8dc831b6e13664fb173c40e690
View on Chainz β†—

Height

#29,818

Difficulty

7.985525

Transactions

1

Size

197 B

Version

2

Bits

07fc4b5a

Nonce

1,121

Timestamp

7/13/2013, 4:50:43 PM

Confirmations

6,766,742

Mined by

⛏️ P2SHAS4Pf5oLcWa2Bm61YMMFth8zvCfdaGq2mN

Merkle Root

6ae3605e6dd30e4a1bda34863e97abfd8276d2161c3ff93d186867cb777c20fc
Transactions (1)
Coinbase6ae3605e6dd30e…6867cb777c20fc
1 in β†’ 1 out15.6600 XPM108 B
AS4Pf5oL…fdaGq2mN
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.

2.682 Γ— 10⁹³(94-digit number)
26820834360573633722…47207570315427685601
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
2.682 Γ— 10⁹³(94-digit number)
26820834360573633722…47207570315427685601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.364 Γ— 10⁹³(94-digit number)
53641668721147267444…94415140630855371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.072 Γ— 10⁹⁴(95-digit number)
10728333744229453488…88830281261710742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.145 Γ— 10⁹⁴(95-digit number)
21456667488458906977…77660562523421484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.291 Γ— 10⁹⁴(95-digit number)
42913334976917813955…55321125046842969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.582 Γ— 10⁹⁴(95-digit number)
85826669953835627910…10642250093685939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.716 Γ— 10⁹⁡(96-digit number)
17165333990767125582…21284500187371878401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.433 Γ— 10⁹⁡(96-digit number)
34330667981534251164…42569000374743756801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,616,479 XPMΒ·at block #6,796,559 Β· updates every 60s
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