Block #438,476

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/11/2014, 12:56:50 AM · Difficulty 10.3572 · 6,356,903 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b03d63dd40b3bcb89f538b6bc8eb063e7bcb3d436833bd8feb23fafa993c8a42

View on Chainz ↗

Height

#438,476

Difficulty

10.357189

Transactions

Size

937 B

Version

Bits

0a5b70b5

Nonce

23,379

Timestamp

3/11/2014, 12:56:50 AM

Confirmations

6,356,903

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

af03e19a3762a5c988891d6e6dea0011062a1396b0f5ef8aa5cfe9d7dd235225

Transactions (1)

Coinbaseaf03e19a3762a5…cfe9d7dd235225

1 in → 23 out9.3100 XPM845 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AQT6GR3K…nYGow82m Adbb4svj…dQWTHsq5 AUFKXvnz…342ApNcm

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.

6.143 × 10⁹⁹(100-digit number)

61431331797557866735…48291156931317852159

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

6.143 × 10⁹⁹(100-digit number)

61431331797557866735…48291156931317852159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.228 × 10¹⁰⁰(101-digit number)

12286266359511573347…96582313862635704319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.457 × 10¹⁰⁰(101-digit number)

24572532719023146694…93164627725271408639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.914 × 10¹⁰⁰(101-digit number)

49145065438046293388…86329255450542817279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.829 × 10¹⁰⁰(101-digit number)

98290130876092586777…72658510901085634559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.965 × 10¹⁰¹(102-digit number)

19658026175218517355…45317021802171269119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.931 × 10¹⁰¹(102-digit number)

39316052350437034710…90634043604342538239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.863 × 10¹⁰¹(102-digit number)

78632104700874069421…81268087208685076479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.572 × 10¹⁰²(103-digit number)

15726420940174813884…62536174417370152959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.145 × 10¹⁰²(103-digit number)

31452841880349627768…25072348834740305919

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