Block #28,410

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 12:12:11 PM · Difficulty 7.9818 · 6,772,632 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

019932bcf1f3ad2ba63d037d016b91ba7ff6e4c60a5578fc1d77cc67fd57e5ef

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Height

#28,410

Difficulty

7.981842

Transactions

Size

203 B

Version

Bits

07fb59fb

Nonce

780

Timestamp

7/13/2013, 12:12:11 PM

Confirmations

6,772,632

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

2aed68aa39a3c2484bb9ec1bc4cee11b81e81ffd34c4ade3b6468e81f74e21c3

Transactions (1)

Coinbase2aed68aa39a3c2…468e81f74e21c3

1 in → 1 out15.6800 XPM108 B

AKSwr9eU…dLNxuVyn

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.

1.016 × 10¹⁰⁷(108-digit number)

10161575101029684810…01276360169505325861

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

1.016 × 10¹⁰⁷(108-digit number)

10161575101029684810…01276360169505325861

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.032 × 10¹⁰⁷(108-digit number)

20323150202059369620…02552720339010651721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.064 × 10¹⁰⁷(108-digit number)

40646300404118739240…05105440678021303441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.129 × 10¹⁰⁷(108-digit number)

81292600808237478480…10210881356042606881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.625 × 10¹⁰⁸(109-digit number)

16258520161647495696…20421762712085213761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.251 × 10¹⁰⁸(109-digit number)

32517040323294991392…40843525424170427521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.503 × 10¹⁰⁸(109-digit number)

65034080646589982784…81687050848340855041

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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