Block #416,120

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/23/2014, 5:06:52 AM · Difficulty 10.3993 · 6,382,777 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

20a26e25c9c1676c87c0fa876c3061a2b8ad8a75c34f899267ba4d7d28023cc5

View on Chainz ↗

Height

#416,120

Difficulty

10.399270

Transactions

Size

937 B

Version

Bits

0a663689

Nonce

7,691

Timestamp

2/23/2014, 5:06:52 AM

Confirmations

6,382,777

Mined by

⛏️ xYaSALqxX1WA4yGGdvvcw46Ggu5ZRhhsKjbnXn

Merkle Root

3ade6b1100cef41b4cf9f6c6b92894071b80c6bac47c279a5b13f0632de2e91f

Transactions (1)

Coinbase3ade6b1100cef4…13f0632de2e91f

1 in → 23 out9.2300 XPM845 B

ALqxX1WA…hsKjbnXn AYtDvcGs…VuAcA7m7 ANNg88pG…ppn21sTe ARSeozDw…C9HtARnj AQwRN8bE…V8PsTcY9

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.

1.411 × 10⁹⁹(100-digit number)

14113646310572721312…36304301756368250879

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

1.411 × 10⁹⁹(100-digit number)

14113646310572721312…36304301756368250879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.822 × 10⁹⁹(100-digit number)

28227292621145442624…72608603512736501759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.645 × 10⁹⁹(100-digit number)

56454585242290885249…45217207025473003519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.129 × 10¹⁰⁰(101-digit number)

11290917048458177049…90434414050946007039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.258 × 10¹⁰⁰(101-digit number)

22581834096916354099…80868828101892014079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.516 × 10¹⁰⁰(101-digit number)

45163668193832708199…61737656203784028159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.032 × 10¹⁰⁰(101-digit number)

90327336387665416398…23475312407568056319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.806 × 10¹⁰¹(102-digit number)

18065467277533083279…46950624815136112639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.613 × 10¹⁰¹(102-digit number)

36130934555066166559…93901249630272225279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.226 × 10¹⁰¹(102-digit number)

72261869110132333118…87802499260544450559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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