Block #268,515

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/22/2013, 5:15:02 AM · Difficulty 9.9569 · 6,533,907 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

468804f2a773b294060a3a5b841464ff895e898dc22611c0a3516cedff6c015a

View on Chainz ↗

Height

#268,515

Difficulty

9.956876

Transactions

Size

685 B

Version

Bits

09f4f5d1

Nonce

12,555

Timestamp

11/22/2013, 5:15:02 AM

Confirmations

6,533,907

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

7df38e723b3d0333fb44ef76ed9c7f06ed328312bf2c1d38c74e0b967d4d7db8

Transactions (3)

Coinbasec794e2ec69ae54…648945fada5322

1 in → 2 out10.0900 XPM142 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

493cb2d024b27b…a86e74e5d5b5f9

1 in → 2 out5.9933 XPM225 B

AWtoDhym…rEeeSQQt AGYbF8A5…P5KCm4Hj

b7fd64f141da7f…ee6b40bfd0dcda

1 in → 2 out2.8791 XPM225 B

AWs2eBzs…Pt5tGg2U AXCCsfyG…SSSFr1ZK

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.

4.264 × 10¹⁰²(103-digit number)

42647972044278377618…93538143969940334599

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

4.264 × 10¹⁰²(103-digit number)

42647972044278377618…93538143969940334599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.529 × 10¹⁰²(103-digit number)

85295944088556755237…87076287939880669199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.705 × 10¹⁰³(104-digit number)

17059188817711351047…74152575879761338399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.411 × 10¹⁰³(104-digit number)

34118377635422702095…48305151759522676799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.823 × 10¹⁰³(104-digit number)

68236755270845404190…96610303519045353599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.364 × 10¹⁰⁴(105-digit number)

13647351054169080838…93220607038090707199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.729 × 10¹⁰⁴(105-digit number)

27294702108338161676…86441214076181414399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.458 × 10¹⁰⁴(105-digit number)

54589404216676323352…72882428152362828799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.091 × 10¹⁰⁵(106-digit number)

10917880843335264670…45764856304725657599

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