Block #48,741

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 4:50:38 PM · Difficulty 8.8512 · 6,747,168 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

52200178a081d59625949049181f2bad44a1a6c287f87a92e69f6aec626ec73d

View on Chainz ↗

Height

#48,741

Difficulty

8.851246

Transactions

Size

364 B

Version

Bits

08d9eb4a

Nonce

1,464

Timestamp

7/15/2013, 4:50:38 PM

Confirmations

6,747,168

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

58e6c637d9a532cd4afe7ff788933f9aad6113317a636891f43f2a2ffc3b30dd

Transactions (2)

Coinbase6073f7afba8687…7009558b80fb3a

1 in → 1 out12.7600 XPM110 B

AcBadmkp…GmhL921o

2c76ffd8e55800…d59ce22f87bfd7

1 in → 1 out13.0000 XPM158 B

AG43TCYA…UW1AUz7e

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.

6.172 × 10¹⁰⁸(109-digit number)

61727245441152725869…81460116073994850481

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

6.172 × 10¹⁰⁸(109-digit number)

61727245441152725869…81460116073994850481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.234 × 10¹⁰⁹(110-digit number)

12345449088230545173…62920232147989700961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.469 × 10¹⁰⁹(110-digit number)

24690898176461090347…25840464295979401921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.938 × 10¹⁰⁹(110-digit number)

49381796352922180695…51680928591958803841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.876 × 10¹⁰⁹(110-digit number)

98763592705844361391…03361857183917607681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.975 × 10¹¹⁰(111-digit number)

19752718541168872278…06723714367835215361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.950 × 10¹¹⁰(111-digit number)

39505437082337744556…13447428735670430721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.901 × 10¹¹⁰(111-digit number)

79010874164675489113…26894857471340861441

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