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Block #670,725

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2014, 7:00:52 PM Β· Difficulty 10.9642 Β· 6,154,590 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
11ef18268f146c9c8e8fbbdb6eaf6ef2cecbf4ab0bb8be207b218a606943d32b
View on Chainz β†—

Height

#670,725

Difficulty

10.964180

Transactions

1

Size

198 B

Version

2

Bits

0af6d486

Nonce

1,117,610,145

Timestamp

8/9/2014, 7:00:52 PM

Confirmations

6,154,590

Mined by

⛏️ P2SHAb57BoUQguXTG7ZXMP7X7HVECdAFWwWqZ6

Merkle Root

cf70a21dc997a97ba14347d1c5718cc34b66139fa9eb5113c83afaa953e7d8d9
Transactions (1)
Coinbasecf70a21dc997a9…3afaa953e7d8d9
1 in β†’ 1 out8.3100 XPM109 B
Ab57BoUQ…AFWwWqZ6
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.

9.390 Γ— 10⁹²(93-digit number)
93903167610828522553…28048907189755795481
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
9.390 Γ— 10⁹²(93-digit number)
93903167610828522553…28048907189755795481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.878 Γ— 10⁹³(94-digit number)
18780633522165704510…56097814379511590961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.756 Γ— 10⁹³(94-digit number)
37561267044331409021…12195628759023181921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.512 Γ— 10⁹³(94-digit number)
75122534088662818042…24391257518046363841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.502 Γ— 10⁹⁴(95-digit number)
15024506817732563608…48782515036092727681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.004 Γ— 10⁹⁴(95-digit number)
30049013635465127217…97565030072185455361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.009 Γ— 10⁹⁴(95-digit number)
60098027270930254434…95130060144370910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.201 Γ— 10⁹⁡(96-digit number)
12019605454186050886…90260120288741821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.403 Γ— 10⁹⁡(96-digit number)
24039210908372101773…80520240577483642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.807 Γ— 10⁹⁡(96-digit number)
48078421816744203547…61040481154967285761
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:57,846,624 XPMΒ·at block #6,825,314 Β· updates every 60s
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