Block #29,798

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 4:46:46 PM · Difficulty 7.9855 · 6,773,574 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

10b4dd88c9c0ba0691e843b69cbeb03a5c1c45b582d4678fbb89d67d18177c02

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Height

#29,798

Difficulty

7.985479

Transactions

Size

208 B

Version

Bits

07fc4853

Nonce

592

Timestamp

7/13/2013, 4:46:46 PM

Confirmations

6,773,574

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

5eaf5e2ee6ea87f06f191686412665c60d520ef5aa7202799047d501b3d61f33

Transactions (1)

Coinbase5eaf5e2ee6ea87…47d501b3d61f33

1 in → 1 out15.6600 XPM108 B

AGemJXng…w1K3MEut

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.

2.362 × 10¹¹⁸(119-digit number)

23629254795644452585…19126326857892366601

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

2.362 × 10¹¹⁸(119-digit number)

23629254795644452585…19126326857892366601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.725 × 10¹¹⁸(119-digit number)

47258509591288905170…38252653715784733201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.451 × 10¹¹⁸(119-digit number)

94517019182577810340…76505307431569466401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.890 × 10¹¹⁹(120-digit number)

18903403836515562068…53010614863138932801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.780 × 10¹¹⁹(120-digit number)

37806807673031124136…06021229726277865601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.561 × 10¹¹⁹(120-digit number)

75613615346062248272…12042459452555731201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.512 × 10¹²⁰(121-digit number)

15122723069212449654…24084918905111462401

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