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Block #452,582

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/20/2014, 4:36:43 PM Β· Difficulty 10.3907 Β· 6,343,938 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
855d8d3be6a3304e7a688922446ff78c6cd4db868ff187e3cb8395b0dd2d82da
View on Chainz β†—

Height

#452,582

Difficulty

10.390676

Transactions

2

Size

6.74 KB

Version

2

Bits

0a640355

Nonce

146,567

Timestamp

3/20/2014, 4:36:43 PM

Confirmations

6,343,938

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c807a8f061642220a15efe146fcc6888f45be71cd82f6e7e02e347eb94da9a93
Transactions (2)
Coinbase88f892ee95f071…d1716cabff9c6b
1 in β†’ 1 out9.3200 XPM110 B
AeKNrjNj…1NEq95Ta
5e4445ad97023c…133c7d0a499a1b
45 in β†’ 1 out14.4876 XPM6.54 KB
AUngfv6y…Q3LTGWVH
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.

9.155 Γ— 10¹⁰⁡(106-digit number)
91551945972695369783…98107314211551185921
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
9.155 Γ— 10¹⁰⁡(106-digit number)
91551945972695369783…98107314211551185921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.831 Γ— 10¹⁰⁢(107-digit number)
18310389194539073956…96214628423102371841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.662 Γ— 10¹⁰⁢(107-digit number)
36620778389078147913…92429256846204743681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.324 Γ— 10¹⁰⁢(107-digit number)
73241556778156295826…84858513692409487361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.464 Γ— 10¹⁰⁷(108-digit number)
14648311355631259165…69717027384818974721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.929 Γ— 10¹⁰⁷(108-digit number)
29296622711262518330…39434054769637949441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.859 Γ— 10¹⁰⁷(108-digit number)
58593245422525036661…78868109539275898881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.171 Γ— 10¹⁰⁸(109-digit number)
11718649084505007332…57736219078551797761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.343 Γ— 10¹⁰⁸(109-digit number)
23437298169010014664…15472438157103595521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.687 Γ— 10¹⁰⁸(109-digit number)
46874596338020029328…30944876314207191041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,616,157 XPMΒ·at block #6,796,519 Β· updates every 60s
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