Block #46,390

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 6:21:28 AM · Difficulty 8.7906 · 6,749,132 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9b98faa6b785e8ba2176140470669a660b623e2033e587e1e033a8a1331f0887

View on Chainz ↗

Height

#46,390

Difficulty

8.790573

Transactions

Size

366 B

Version

Bits

08ca6302

Nonce

302

Timestamp

7/15/2013, 6:21:28 AM

Confirmations

6,749,132

Mined by

⛏️ P2SHARmdRhtUuwMWwY2ZtR7cbjHpGkCB9T8RqH

Merkle Root

2d68957c2a26e7cda340993316c85d213fc796df020a20dca58d8013600df461

Transactions (2)

Coinbase34b35e8cd8114b…fad52e78e19758

1 in → 1 out12.9300 XPM110 B

ARmdRhtU…CB9T8RqH

4e9ebfa328b732…923b1c3ce6c440

1 in → 1 out13.4900 XPM159 B

AScNu17i…EEtEnKS9

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.

4.780 × 10¹¹⁰(111-digit number)

47802880294347367924…07701321638452469751

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

4.780 × 10¹¹⁰(111-digit number)

47802880294347367924…07701321638452469751

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.560 × 10¹¹⁰(111-digit number)

95605760588694735849…15402643276904939501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.912 × 10¹¹¹(112-digit number)

19121152117738947169…30805286553809879001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.824 × 10¹¹¹(112-digit number)

38242304235477894339…61610573107619758001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.648 × 10¹¹¹(112-digit number)

76484608470955788679…23221146215239516001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.529 × 10¹¹²(113-digit number)

15296921694191157735…46442292430479032001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.059 × 10¹¹²(113-digit number)

30593843388382315471…92884584860958064001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.118 × 10¹¹²(113-digit number)

61187686776764630943…85769169721916128001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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