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Block #345,893

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/6/2014, 5:45:35 AM Β· Difficulty 10.2136 Β· 6,478,905 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7cbe62d25bf0af6ecc04ebcd66865367f5b2fc83749e2bad08240c7b2df3f376
View on Chainz β†—

Height

#345,893

Difficulty

10.213564

Transactions

1

Size

198 B

Version

2

Bits

0a36ac29

Nonce

143,966

Timestamp

1/6/2014, 5:45:35 AM

Confirmations

6,478,905

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

3dd97dea60c33d8af3f0fa4efe424c20be5aa0053ae4d826961bb31fd3163cb3
Transactions (1)
Coinbase3dd97dea60c33d…1bb31fd3163cb3
1 in β†’ 1 out9.5700 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.

1.292 Γ— 10⁹¹(92-digit number)
12922523731538779936…46719872882705299201
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
1.292 Γ— 10⁹¹(92-digit number)
12922523731538779936…46719872882705299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.584 Γ— 10⁹¹(92-digit number)
25845047463077559872…93439745765410598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.169 Γ— 10⁹¹(92-digit number)
51690094926155119744…86879491530821196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.033 Γ— 10⁹²(93-digit number)
10338018985231023948…73758983061642393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.067 Γ— 10⁹²(93-digit number)
20676037970462047897…47517966123284787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.135 Γ— 10⁹²(93-digit number)
41352075940924095795…95035932246569574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.270 Γ— 10⁹²(93-digit number)
82704151881848191591…90071864493139148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.654 Γ— 10⁹³(94-digit number)
16540830376369638318…80143728986278297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.308 Γ— 10⁹³(94-digit number)
33081660752739276636…60287457972556595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.616 Γ— 10⁹³(94-digit number)
66163321505478553272…20574915945113190401
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:57,842,460 XPMΒ·at block #6,824,797 Β· updates every 60s
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