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Block #375,659

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/25/2014, 8:59:28 PM Β· Difficulty 10.4243 Β· 6,469,468 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d6369f17e94772ec138bd0f6bef0f7e71376367f58d11e67828139c12059f942
View on Chainz β†—

Height

#375,659

Difficulty

10.424319

Transactions

1

Size

205 B

Version

2

Bits

0a6ca026

Nonce

26

Timestamp

1/25/2014, 8:59:28 PM

Confirmations

6,469,468

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a8a75afd8837340edabd998ba3a9141cb6dddb3a396983748d40a29e386f98d1
Transactions (1)
Coinbasea8a75afd883734…40a29e386f98d1
1 in β†’ 1 out9.1900 XPM116 B
AbwWkWZt…kawDhufa
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.

5.936 Γ— 10⁹²(93-digit number)
59368668229327171035…47585937864510612341
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
5.936 Γ— 10⁹²(93-digit number)
59368668229327171035…47585937864510612341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.187 Γ— 10⁹³(94-digit number)
11873733645865434207…95171875729021224681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.374 Γ— 10⁹³(94-digit number)
23747467291730868414…90343751458042449361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.749 Γ— 10⁹³(94-digit number)
47494934583461736828…80687502916084898721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.498 Γ— 10⁹³(94-digit number)
94989869166923473656…61375005832169797441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.899 Γ— 10⁹⁴(95-digit number)
18997973833384694731…22750011664339594881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.799 Γ— 10⁹⁴(95-digit number)
37995947666769389462…45500023328679189761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.599 Γ— 10⁹⁴(95-digit number)
75991895333538778924…91000046657358379521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.519 Γ— 10⁹⁡(96-digit number)
15198379066707755784…82000093314716759041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.039 Γ— 10⁹⁡(96-digit number)
30396758133415511569…64000186629433518081
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:58,005,443 XPMΒ·at block #6,845,126 Β· updates every 60s
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