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Block #29,246

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 2:52:43 PM Β· Difficulty 7.9841 Β· 6,766,051 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c9c650916331ffdce82a5b16efd16c686b390b08b5dc3ec9b0b8dfbf2da37f19
View on Chainz β†—

Height

#29,246

Difficulty

7.984142

Transactions

1

Size

200 B

Version

2

Bits

07fbf0b9

Nonce

191

Timestamp

7/13/2013, 2:52:43 PM

Confirmations

6,766,051

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

6fc6c0e537a78596539d59bacf0e5cd78f001d5e64225b5de1d86e82616ecf38
Transactions (1)
Coinbase6fc6c0e537a785…d86e82616ecf38
1 in β†’ 1 out15.6700 XPM109 B
AGemJXng…w1K3MEut
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.

1.061 Γ— 10⁹⁸(99-digit number)
10615472290584697640…44076142299125782931
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
1.061 Γ— 10⁹⁸(99-digit number)
10615472290584697640…44076142299125782931
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.123 Γ— 10⁹⁸(99-digit number)
21230944581169395281…88152284598251565861
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.246 Γ— 10⁹⁸(99-digit number)
42461889162338790562…76304569196503131721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.492 Γ— 10⁹⁸(99-digit number)
84923778324677581124…52609138393006263441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.698 Γ— 10⁹⁹(100-digit number)
16984755664935516224…05218276786012526881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.396 Γ— 10⁹⁹(100-digit number)
33969511329871032449…10436553572025053761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.793 Γ— 10⁹⁹(100-digit number)
67939022659742064899…20873107144050107521
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,606,428 XPMΒ·at block #6,795,296 Β· updates every 60s
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