Block #56,639

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/17/2013, 9:23:04 AM · Difficulty 8.9499 · 6,748,370 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

61b3a03cd6ecbb5c4c519350e0ee9de5d67422be5d691e1a2c64a9686a75f219

View on Chainz ↗

Height

#56,639

Difficulty

8.949851

Transactions

Size

198 B

Version

Bits

08f32970

Nonce

332

Timestamp

7/17/2013, 9:23:04 AM

Confirmations

6,748,370

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

e3eb6f671dd5abaa0c21519d3337c97d8cf21955f6cbc398c0fd203e0223cf6a

Transactions (1)

Coinbasee3eb6f671dd5ab…fd203e0223cf6a

1 in → 1 out12.4700 XPM110 B

AeTcmmqH…LrFchfe1

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.

9.427 × 10⁸⁹(90-digit number)

94270939235186042939…44199415102964172389

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

9.427 × 10⁸⁹(90-digit number)

94270939235186042939…44199415102964172389

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.885 × 10⁹⁰(91-digit number)

18854187847037208587…88398830205928344779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.770 × 10⁹⁰(91-digit number)

37708375694074417175…76797660411856689559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.541 × 10⁹⁰(91-digit number)

75416751388148834351…53595320823713379119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.508 × 10⁹¹(92-digit number)

15083350277629766870…07190641647426758239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.016 × 10⁹¹(92-digit number)

30166700555259533740…14381283294853516479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.033 × 10⁹¹(92-digit number)

60333401110519067481…28762566589707032959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.206 × 10⁹²(93-digit number)

12066680222103813496…57525133179414065919

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 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 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 1CC formula:

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

Cross-reference on Chainz Explorer