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Block #347,833

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/7/2014, 11:08:27 AM Β· Difficulty 10.2415 Β· 6,462,245 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eaa90e575708704df7fb3db2ce41495d238f4d71ffd9ed9edd81d661d480de64
View on Chainz β†—

Height

#347,833

Difficulty

10.241488

Transactions

1

Size

201 B

Version

2

Bits

0a3dd22f

Nonce

92,060

Timestamp

1/7/2014, 11:08:27 AM

Confirmations

6,462,245

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

765d795cd4e6266c4e7152a5d3ff5b839bebab054bda6d19fb5cf0e6be98d4d6
Transactions (1)
Coinbase765d795cd4e626…5cf0e6be98d4d6
1 in β†’ 1 out9.5200 XPM110 B
AeKNrjNj…1NEq95Ta
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.

6.294 Γ— 10⁹⁢(97-digit number)
62948208442640555071…26403196430046630201
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
6.294 Γ— 10⁹⁢(97-digit number)
62948208442640555071…26403196430046630201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.258 Γ— 10⁹⁷(98-digit number)
12589641688528111014…52806392860093260401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.517 Γ— 10⁹⁷(98-digit number)
25179283377056222028…05612785720186520801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.035 Γ— 10⁹⁷(98-digit number)
50358566754112444057…11225571440373041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10071713350822488811…22451142880746083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.014 Γ— 10⁹⁸(99-digit number)
20143426701644977622…44902285761492166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.028 Γ— 10⁹⁸(99-digit number)
40286853403289955245…89804571522984332801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.057 Γ— 10⁹⁸(99-digit number)
80573706806579910491…79609143045968665601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.611 Γ— 10⁹⁹(100-digit number)
16114741361315982098…59218286091937331201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.222 Γ— 10⁹⁹(100-digit number)
32229482722631964196…18436572183874662401
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:57,724,696 XPMΒ·at block #6,810,077 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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