Block #305,615

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2013, 2:31:48 PM · Difficulty 9.9936 · 6,487,969 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6d7e6f27ebb8448f7da5bd9905f479f131ccd738b215348cb191c86838690416

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Height

#305,615

Difficulty

9.993638

Transactions

Size

1.08 KB

Version

Bits

09fe5f0d

Nonce

53,407

Timestamp

12/11/2013, 2:31:48 PM

Confirmations

6,487,969

Merkle Root

604abe67c495c8917f5066b5916aa3277a0cc3505d9253b2fcbbc9add7243655

Transactions (1)

Coinbase604abe67c495c8…bbc9add7243655

1 in → 28 out9.9800 XPM1015 B

AHuJ9wYh…BGmgHrKZ AZ2pPuKg…95SN2Yr7 Ae6gEbs5…m5Mn8oYw ASWX42VM…XypQABkY ATiP2myP…qVUH8Grb

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.

8.835 × 10⁹¹(92-digit number)

88355890668473970496…86039780697720142081

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

8.835 × 10⁹¹(92-digit number)

88355890668473970496…86039780697720142081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.767 × 10⁹²(93-digit number)

17671178133694794099…72079561395440284161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.534 × 10⁹²(93-digit number)

35342356267389588198…44159122790880568321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.068 × 10⁹²(93-digit number)

70684712534779176397…88318245581761136641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.413 × 10⁹³(94-digit number)

14136942506955835279…76636491163522273281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.827 × 10⁹³(94-digit number)

28273885013911670558…53272982327044546561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.654 × 10⁹³(94-digit number)

56547770027823341117…06545964654089093121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.130 × 10⁹⁴(95-digit number)

11309554005564668223…13091929308178186241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.261 × 10⁹⁴(95-digit number)

22619108011129336447…26183858616356372481

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 × 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