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Block #392,686

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/6/2014, 3:10:14 PM Β· Difficulty 10.4403 Β· 6,434,071 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fa1e6417a57202be66937ba924199322a027fe129eae720f8c69ed3fc5265623
View on Chainz β†—

Height

#392,686

Difficulty

10.440344

Transactions

2

Size

413 B

Version

2

Bits

0a70ba5d

Nonce

109,257

Timestamp

2/6/2014, 3:10:14 PM

Confirmations

6,434,071

Mined by

⛏️ aRAbMAHMS8edmSw9jhkJ2fCCZzvKMwEzMSoj

Merkle Root

1e95d2b9064f90b9c3ca7b2e0b789de996c7fad8ac90730d4a7be942f5ba72f8
Transactions (2)
Coinbasea987a822cff76b…c738121af950cf
1 in β†’ 1 out9.1600 XPM97 B
AbMAHMS8…MwEzMSoj
1ad7115b5f1cb7…6a6ef0e91515d8
1 in β†’ 2 out46.9240 XPM226 B
AZQexp7g…DUqJ66i3AGhqx9U2…jxFM6Bm6
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.

1.271 Γ— 10⁹⁴(95-digit number)
12717059113594401130…17061156896021260801
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
1.271 Γ— 10⁹⁴(95-digit number)
12717059113594401130…17061156896021260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.543 Γ— 10⁹⁴(95-digit number)
25434118227188802260…34122313792042521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.086 Γ— 10⁹⁴(95-digit number)
50868236454377604521…68244627584085043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.017 Γ— 10⁹⁡(96-digit number)
10173647290875520904…36489255168170086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.034 Γ— 10⁹⁡(96-digit number)
20347294581751041808…72978510336340172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.069 Γ— 10⁹⁡(96-digit number)
40694589163502083616…45957020672680345601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.138 Γ— 10⁹⁡(96-digit number)
81389178327004167233…91914041345360691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.627 Γ— 10⁹⁢(97-digit number)
16277835665400833446…83828082690721382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.255 Γ— 10⁹⁢(97-digit number)
32555671330801666893…67656165381442764801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.511 Γ— 10⁹⁢(97-digit number)
65111342661603333786…35312330762885529601
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:57,858,214 XPMΒ·at block #6,826,756 Β· updates every 60s
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