Block #79,780

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 5:38:39 PM · Difficulty 9.2437 · 6,715,210 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1e022ea4453df7213123d28c4bffd16c505aaa8cee57996024cc67d05be07db0

View on Chainz ↗

Height

#79,780

Difficulty

9.243736

Transactions

Size

580 B

Version

Bits

093e657a

Nonce

439

Timestamp

7/23/2013, 5:38:39 PM

Confirmations

6,715,210

Mined by

⛏️ P2SHAGME8xkT6rhoYKptywtyLaFKWJiv5eRbEh

Merkle Root

bebcbb0abaf541e0ca46920e42f0ee5e8fb38663597fa09e1b06f36aed47db8f

Transactions (2)

Coinbasebfcdc6938d6ced…e4649f2b51fd35

1 in → 1 out11.7000 XPM110 B

AGME8xkT…iv5eRbEh

2dd14ae15316b6…bed521337be1f5

2 in → 2 out125.2598 XPM376 B

AdCWiuKv…MWT5Bto8 AKKb38vw…nN1DKpfW

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.

6.193 × 10¹⁰³(104-digit number)

61938568559957730648…81988932403037849001

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

6.193 × 10¹⁰³(104-digit number)

61938568559957730648…81988932403037849001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.238 × 10¹⁰⁴(105-digit number)

12387713711991546129…63977864806075698001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.477 × 10¹⁰⁴(105-digit number)

24775427423983092259…27955729612151396001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.955 × 10¹⁰⁴(105-digit number)

49550854847966184518…55911459224302792001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.910 × 10¹⁰⁴(105-digit number)

99101709695932369037…11822918448605584001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.982 × 10¹⁰⁵(106-digit number)

19820341939186473807…23645836897211168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.964 × 10¹⁰⁵(106-digit number)

39640683878372947615…47291673794422336001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.928 × 10¹⁰⁵(106-digit number)

79281367756745895230…94583347588844672001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.585 × 10¹⁰⁶(107-digit number)

15856273551349179046…89166695177689344001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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