Block #84,135

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 3:09:23 PM · Difficulty 9.2713 · 6,714,470 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

06cded5726e17890727d3ce08a962b6f45fecf47917807ea8dd52cbd4598fd6d

View on Chainz ↗

Height

#84,135

Difficulty

9.271342

Transactions

Size

361 B

Version

Bits

094576a7

Nonce

950

Timestamp

7/26/2013, 3:09:23 PM

Confirmations

6,714,470

Mined by

⛏️ P2SHASRQWarMreqSce3LDsC7BPQW8A3sVUPMLr

Merkle Root

6b994066d9350c31fcc725e07c0bb0b81fd65d7f3fa89b371456446f3b15e90e

Transactions (2)

Coinbase4e6c026b020792…37826909e148fd

1 in → 1 out11.6300 XPM110 B

ASRQWarM…3sVUPMLr

c79d35b3ef893c…d0cbfcee5e408f

1 in → 1 out11.6600 XPM159 B

AaGrdg3x…FpKQ8mir

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.

9.414 × 10⁹⁹(100-digit number)

94147408405150978729…55745913207607649099

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

9.414 × 10⁹⁹(100-digit number)

94147408405150978729…55745913207607649099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.882 × 10¹⁰⁰(101-digit number)

18829481681030195745…11491826415215298199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.765 × 10¹⁰⁰(101-digit number)

37658963362060391491…22983652830430596399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.531 × 10¹⁰⁰(101-digit number)

75317926724120782983…45967305660861192799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.506 × 10¹⁰¹(102-digit number)

15063585344824156596…91934611321722385599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.012 × 10¹⁰¹(102-digit number)

30127170689648313193…83869222643444771199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.025 × 10¹⁰¹(102-digit number)

60254341379296626387…67738445286889542399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.205 × 10¹⁰²(103-digit number)

12050868275859325277…35476890573779084799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.410 × 10¹⁰²(103-digit number)

24101736551718650554…70953781147558169599

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