Block #83,266

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 12:49:49 AM · Difficulty 9.2697 · 6,734,334 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

dc0e6f96290801868bd79f2799b2ee0006547a7fdb2afafd6ebb2c58352a0c87

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Height

#83,266

Difficulty

9.269700

Transactions

Size

202 B

Version

Bits

09450b0c

Nonce

376,711

Timestamp

7/26/2013, 12:49:49 AM

Confirmations

6,734,334

Mined by

⛏️ P2SHAc3AUHowoddp8FyKEjyx2vqHMdhYeSm7Mw

Merkle Root

6efe1e29e6f1ed7a4dcecbdaac47c1eb2010ce183b82705690a418e3de278b56

Transactions (1)

Coinbase6efe1e29e6f1ed…a418e3de278b56

1 in → 1 out11.6200 XPM109 B

Ac3AUHow…hYeSm7Mw

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.

4.260 × 10¹⁰¹(102-digit number)

42602474068883373802…15379194259953487459

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

4.260 × 10¹⁰¹(102-digit number)

42602474068883373802…15379194259953487459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.520 × 10¹⁰¹(102-digit number)

85204948137766747604…30758388519906974919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.704 × 10¹⁰²(103-digit number)

17040989627553349520…61516777039813949839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.408 × 10¹⁰²(103-digit number)

34081979255106699041…23033554079627899679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.816 × 10¹⁰²(103-digit number)

68163958510213398083…46067108159255799359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.363 × 10¹⁰³(104-digit number)

13632791702042679616…92134216318511598719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.726 × 10¹⁰³(104-digit number)

27265583404085359233…84268432637023197439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.453 × 10¹⁰³(104-digit number)

54531166808170718467…68536865274046394879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.090 × 10¹⁰⁴(105-digit number)

10906233361634143693…37073730548092789759

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

Block #83,266

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