Block #106,894

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/9/2013, 6:00:18 AM · Difficulty 9.6178 · 6,684,261 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

671771cae687a4b2a64b3e26d8a179c23e091761f3dc3753761f721a763302b0

View on Chainz ↗

Height

#106,894

Difficulty

9.617795

Transactions

Size

202 B

Version

Bits

099e27d7

Nonce

2,408

Timestamp

8/9/2013, 6:00:18 AM

Confirmations

6,684,261

Merkle Root

b456c2d3c8e4c5983873e4324d27c84ad49e1e5ed8d640b5e8e85f742b62487a

Transactions (1)

Coinbaseb456c2d3c8e4c5…e85f742b62487a

1 in → 1 out10.7900 XPM109 B

AWuDuxGX…tLDpHWp7

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.

6.590 × 10¹⁰¹(102-digit number)

65904446444704566564…75348217175668310259

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

6.590 × 10¹⁰¹(102-digit number)

65904446444704566564…75348217175668310259

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.318 × 10¹⁰²(103-digit number)

13180889288940913312…50696434351336620519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.636 × 10¹⁰²(103-digit number)

26361778577881826625…01392868702673241039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.272 × 10¹⁰²(103-digit number)

52723557155763653251…02785737405346482079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.054 × 10¹⁰³(104-digit number)

10544711431152730650…05571474810692964159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.108 × 10¹⁰³(104-digit number)

21089422862305461300…11142949621385928319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.217 × 10¹⁰³(104-digit number)

42178845724610922601…22285899242771856639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.435 × 10¹⁰³(104-digit number)

84357691449221845202…44571798485543713279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.687 × 10¹⁰⁴(105-digit number)

16871538289844369040…89143596971087426559

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