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Block #51,529

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 6:13:42 AM Β· Difficulty 8.8997 Β· 6,762,770 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8cb434d3b881210fb4f3cf50cc7c1b4ba882ad3f00e4a462499ce52fd032626e
View on Chainz β†—

Height

#51,529

Difficulty

8.899730

Transactions

1

Size

198 B

Version

2

Bits

08e654b0

Nonce

186

Timestamp

7/16/2013, 6:13:42 AM

Confirmations

6,762,770

Mined by

⛏️ P2SHAad6DftivGajugTt7GwLT61tYm3wP7iQmg

Merkle Root

539e6e5ab3dbe65c97598274b15c304df2b0fbf3e4f21b31b446c820a968abc7
Transactions (1)
Coinbase539e6e5ab3dbe6…46c820a968abc7
1 in β†’ 1 out12.6100 XPM110 B
Aad6Dfti…3wP7iQmg
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.

1.223 Γ— 10⁹⁰(91-digit number)
12233103221671350784…44473432572512542001
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
1.223 Γ— 10⁹⁰(91-digit number)
12233103221671350784…44473432572512542001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.446 Γ— 10⁹⁰(91-digit number)
24466206443342701569…88946865145025084001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.893 Γ— 10⁹⁰(91-digit number)
48932412886685403138…77893730290050168001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.786 Γ— 10⁹⁰(91-digit number)
97864825773370806277…55787460580100336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.957 Γ— 10⁹¹(92-digit number)
19572965154674161255…11574921160200672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.914 Γ— 10⁹¹(92-digit number)
39145930309348322510…23149842320401344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.829 Γ— 10⁹¹(92-digit number)
78291860618696645021…46299684640802688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.565 Γ— 10⁹²(93-digit number)
15658372123739329004…92599369281605376001
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:57,758,456 XPMΒ·at block #6,814,298 Β· updates every 60s
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