Block #297,183

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/6/2013, 11:22:04 AM · Difficulty 9.9919 · 6,508,031 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c58b406e08bbf8c324c810738055812df6ebf5a337194d4b7618632c1e3583f3

View on Chainz ↗

Height

#297,183

Difficulty

9.991889

Transactions

Size

1.11 KB

Version

Bits

09fdec76

Nonce

1,299

Timestamp

12/6/2013, 11:22:04 AM

Confirmations

6,508,031

Mined by

⛏️ aR'AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

20794c2ee53bf3d38644c6620d9ebebe67efa9420d059a1c6b4fb8d27aecfbef

Transactions (1)

Coinbase20794c2ee53bf3…4fb8d27aecfbef

1 in → 29 out9.9800 XPM1.02 KB

AHuJ9wYh…BGmgHrKZ Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7 AJzWx2VD…j4ZSMit5 AenXgLL6…ChwZjYpX

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.213 × 10⁹⁸(99-digit number)

32131840110651710743…94771096049880678401

Discovered Prime Numbers

p_k = 2^k × 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.

origin + 1

3.213 × 10⁹⁸(99-digit number)

32131840110651710743…94771096049880678401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.426 × 10⁹⁸(99-digit number)

64263680221303421486…89542192099761356801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.285 × 10⁹⁹(100-digit number)

12852736044260684297…79084384199522713601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.570 × 10⁹⁹(100-digit number)

25705472088521368594…58168768399045427201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.141 × 10⁹⁹(100-digit number)

51410944177042737189…16337536798090854401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.028 × 10¹⁰⁰(101-digit number)

10282188835408547437…32675073596181708801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.056 × 10¹⁰⁰(101-digit number)

20564377670817094875…65350147192363417601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.112 × 10¹⁰⁰(101-digit number)

41128755341634189751…30700294384726835201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.225 × 10¹⁰⁰(101-digit number)

82257510683268379502…61400588769453670401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.645 × 10¹⁰¹(102-digit number)

16451502136653675900…22801177538907340801

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer