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Block #16,725

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2013, 11:27:15 PM Β· Difficulty 7.8798 Β· 6,782,617 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c4c6fbd6ad2a41db1d19ebea9a48f34f23a6616cf0d0190b074d20cea0aa6d23
View on Chainz β†—

Height

#16,725

Difficulty

7.879848

Transactions

1

Size

197 B

Version

2

Bits

07e13db6

Nonce

224

Timestamp

7/11/2013, 11:27:15 PM

Confirmations

6,782,617

Mined by

⛏️ P2SHAPKjpCjWikfAJZCrYvw6FmRWiKSL8JjC58

Merkle Root

0ceb8e12cf77095a4709199fb8937724392011eca8c268df4ab59703f5882c76
Transactions (1)
Coinbase0ceb8e12cf7709…b59703f5882c76
1 in β†’ 1 out16.0800 XPM108 B
APKjpCjW…SL8JjC58
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.

1.980 Γ— 10⁹³(94-digit number)
19805021933351619827…79617966137106027621
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
1.980 Γ— 10⁹³(94-digit number)
19805021933351619827…79617966137106027621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.961 Γ— 10⁹³(94-digit number)
39610043866703239654…59235932274212055241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.922 Γ— 10⁹³(94-digit number)
79220087733406479309…18471864548424110481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.584 Γ— 10⁹⁴(95-digit number)
15844017546681295861…36943729096848220961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.168 Γ— 10⁹⁴(95-digit number)
31688035093362591723…73887458193696441921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.337 Γ— 10⁹⁴(95-digit number)
63376070186725183447…47774916387392883841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.267 Γ— 10⁹⁡(96-digit number)
12675214037345036689…95549832774785767681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,638,787 XPMΒ·at block #6,799,341 Β· updates every 60s
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