Block #69,301

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 8:06:07 AM · Difficulty 8.9908 · 6,726,386 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c6fadd21aa400771910d945206518bca14e907f1a2780be9309a0d3a8146636f

View on Chainz ↗

Height

#69,301

Difficulty

8.990752

Transactions

Size

392 B

Version

Bits

08fda1ee

Nonce

274

Timestamp

7/20/2013, 8:06:07 AM

Confirmations

6,726,386

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

3cd7e309faa97c163f1845b278ed77ad6cc77d1e4fb712bd214c7925f0ed016f

Transactions (2)

Coinbase7f41f63b5beece…b45b258b35a6e5

1 in → 1 out12.3600 XPM110 B

AXSFye4r…ADf1YWCU

2df0ca1e2323f2…dfacd539467744

1 in → 2 out12.4400 XPM192 B

AZ2JCM76…Bx4EVVb7 ANtBhPVM…TmEYArZs

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.

1.231 × 10⁹⁴(95-digit number)

12311962146450243661…01751513903100727761

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

1.231 × 10⁹⁴(95-digit number)

12311962146450243661…01751513903100727761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.462 × 10⁹⁴(95-digit number)

24623924292900487323…03503027806201455521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.924 × 10⁹⁴(95-digit number)

49247848585800974647…07006055612402911041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.849 × 10⁹⁴(95-digit number)

98495697171601949295…14012111224805822081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.969 × 10⁹⁵(96-digit number)

19699139434320389859…28024222449611644161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.939 × 10⁹⁵(96-digit number)

39398278868640779718…56048444899223288321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.879 × 10⁹⁵(96-digit number)

78796557737281559436…12096889798446576641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.575 × 10⁹⁶(97-digit number)

15759311547456311887…24193779596893153281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.151 × 10⁹⁶(97-digit number)

31518623094912623774…48387559193786306561

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