Block #244,536

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/4/2013, 10:26:02 PM · Difficulty 9.9630 · 6,558,086 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

98ff376a31420358c8ac74cf137231b993517ac1aff0320321a50bb1a6e812c8

View on Chainz ↗

Height

#244,536

Difficulty

9.963015

Transactions

Size

427 B

Version

Bits

09f6882a

Nonce

1,454

Timestamp

11/4/2013, 10:26:02 PM

Confirmations

6,558,086

Mined by

⛏️ P2SHAaC7FfYJ3wgrxGC78ZvTmB5mToNd6BeiX3

Merkle Root

5a7cbdad2779a2c5678bd4fc672fc500f4daa4d26008d890c38b0cb35a53286b

Transactions (2)

Coinbasef9ced78c610c1c…c9361057daa01a

1 in → 1 out10.0700 XPM109 B

AaC7FfYJ…Nd6BeiX3

5304b0a599b397…4c90011b9ea78e

1 in → 2 out0.0202 XPM225 B

AH3NiLWL…B2Bfryfo AKDVkmGq…sLZwRq5C

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.

1.763 × 10¹⁰²(103-digit number)

17637967550696960387…61952120479438181599

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

1.763 × 10¹⁰²(103-digit number)

17637967550696960387…61952120479438181599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.527 × 10¹⁰²(103-digit number)

35275935101393920775…23904240958876363199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.055 × 10¹⁰²(103-digit number)

70551870202787841551…47808481917752726399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.411 × 10¹⁰³(104-digit number)

14110374040557568310…95616963835505452799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.822 × 10¹⁰³(104-digit number)

28220748081115136620…91233927671010905599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.644 × 10¹⁰³(104-digit number)

56441496162230273241…82467855342021811199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.128 × 10¹⁰⁴(105-digit number)

11288299232446054648…64935710684043622399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.257 × 10¹⁰⁴(105-digit number)

22576598464892109296…29871421368087244799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.515 × 10¹⁰⁴(105-digit number)

45153196929784218593…59742842736174489599

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