Block #57,638

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/17/2013, 3:57:26 PM · Difficulty 8.9555 · 6,758,954 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a6fcd99eeab64a6f5bdafeae4787d03c10d76c81f854144d46eb99e590a06a06

View on Chainz ↗

Height

#57,638

Difficulty

8.955549

Transactions

Size

204 B

Version

Bits

08f49ee4

Nonce

478

Timestamp

7/17/2013, 3:57:26 PM

Confirmations

6,758,954

Mined by

⛏️ P2SHAcuRhoVunZmd7TM7Neh2VRFvWv6Pu86km9

Merkle Root

3ead6b0cca2ba68911afa84ceca1880d9afdb8a619cc8a7f9b8cbf86bc579212

Transactions (1)

Coinbase3ead6b0cca2ba6…8cbf86bc579212

1 in → 1 out12.4500 XPM109 B

AcuRhoVu…6Pu86km9

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.

1.914 × 10¹⁰⁷(108-digit number)

19147796383872531419…80826780901671074131

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

1.914 × 10¹⁰⁷(108-digit number)

19147796383872531419…80826780901671074131

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.829 × 10¹⁰⁷(108-digit number)

38295592767745062838…61653561803342148261

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.659 × 10¹⁰⁷(108-digit number)

76591185535490125676…23307123606684296521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.531 × 10¹⁰⁸(109-digit number)

15318237107098025135…46614247213368593041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.063 × 10¹⁰⁸(109-digit number)

30636474214196050270…93228494426737186081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.127 × 10¹⁰⁸(109-digit number)

61272948428392100540…86456988853474372161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.225 × 10¹⁰⁹(110-digit number)

12254589685678420108…72913977706948744321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.450 × 10¹⁰⁹(110-digit number)

24509179371356840216…45827955413897488641

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

Block #57,638

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