Block #311,983

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/14/2013, 7:44:39 PM · Difficulty 9.9957 · 6,514,873 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

66f0df41796c5461b1eb4223be475914ef2db894b7c1962007e0526a8de4aef5

View on Chainz ↗

Height

#311,983

Difficulty

9.995662

Transactions

Size

208 B

Version

Bits

09fee3b2

Nonce

21,955

Timestamp

12/14/2013, 7:44:39 PM

Confirmations

6,514,873

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

40dace6597fcae2a55d70651e42fd405de73939476363a8da964eeacd1aa7dc9

Transactions (1)

Coinbase40dace6597fcae…64eeacd1aa7dc9

1 in → 1 out9.9900 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) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.713 × 10⁹⁹(100-digit number)

27134102286034186885…61764593793842667521

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

2.713 × 10⁹⁹(100-digit number)

27134102286034186885…61764593793842667521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.426 × 10⁹⁹(100-digit number)

54268204572068373770…23529187587685335041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.085 × 10¹⁰⁰(101-digit number)

10853640914413674754…47058375175370670081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.170 × 10¹⁰⁰(101-digit number)

21707281828827349508…94116750350741340161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.341 × 10¹⁰⁰(101-digit number)

43414563657654699016…88233500701482680321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.682 × 10¹⁰⁰(101-digit number)

86829127315309398032…76467001402965360641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.736 × 10¹⁰¹(102-digit number)

17365825463061879606…52934002805930721281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.473 × 10¹⁰¹(102-digit number)

34731650926123759212…05868005611861442561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.946 × 10¹⁰¹(102-digit number)

69463301852247518425…11736011223722885121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.389 × 10¹⁰²(103-digit number)

13892660370449503685…23472022447445770241

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

Block #311,983

Cookie Preferences