Block #79,807

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/23/2013, 6:06:52 PM · Difficulty 9.2434 · 6,712,966 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6ad0b1fe8de8d64259b71037b29f5c1f7ba6ccb287174eba6b06a6e63c65112d

View on Chainz ↗

Height

#79,807

Difficulty

9.243380

Transactions

Size

206 B

Version

Bits

093e4e23

Nonce

622

Timestamp

7/23/2013, 6:06:52 PM

Confirmations

6,712,966

Merkle Root

fb0689668c59216c7df7240809e4942d114eb13f3a3ed9aa548b4713b655cfa7

Transactions (1)

Coinbasefb0689668c5921…8b4713b655cfa7

1 in → 1 out11.6900 XPM110 B

AHLsLXLf…bdUKx62s

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.

1.242 × 10¹⁰⁹(110-digit number)

12422289374690709795…33937050223142974469

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

1.242 × 10¹⁰⁹(110-digit number)

12422289374690709795…33937050223142974469

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.484 × 10¹⁰⁹(110-digit number)

24844578749381419590…67874100446285948939

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.968 × 10¹⁰⁹(110-digit number)

49689157498762839180…35748200892571897879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.937 × 10¹⁰⁹(110-digit number)

99378314997525678360…71496401785143795759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.987 × 10¹¹⁰(111-digit number)

19875662999505135672…42992803570287591519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.975 × 10¹¹⁰(111-digit number)

39751325999010271344…85985607140575183039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.950 × 10¹¹⁰(111-digit number)

79502651998020542688…71971214281150366079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.590 × 10¹¹¹(112-digit number)

15900530399604108537…43942428562300732159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.180 × 10¹¹¹(112-digit number)

31801060799208217075…87884857124601464319

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer