Block #479,511

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/7/2014, 5:37:35 PM · Difficulty 10.5082 · 6,326,845 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

96507b2378d80b364206ab04f825e49b1eec520d3cdcafd165d122c696df0f6c

View on Chainz ↗

Height

#479,511

Difficulty

10.508236

Transactions

Size

209 B

Version

Bits

0a821bc9

Nonce

423

Timestamp

4/7/2014, 5:37:35 PM

Confirmations

6,326,845

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

975aeef4138cfe85a8ae5ad3330d932c44293bda0bc86ece09a93ce1c3d95ec2

Transactions (1)

Coinbase975aeef4138cfe…a93ce1c3d95ec2

1 in → 1 out9.0400 XPM116 B

AbwWkWZt…kawDhufa

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.

1.538 × 10¹⁰¹(102-digit number)

15386599320192403418…11813357894031523999

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

1.538 × 10¹⁰¹(102-digit number)

15386599320192403418…11813357894031523999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.077 × 10¹⁰¹(102-digit number)

30773198640384806837…23626715788063047999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.154 × 10¹⁰¹(102-digit number)

61546397280769613675…47253431576126095999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.230 × 10¹⁰²(103-digit number)

12309279456153922735…94506863152252191999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.461 × 10¹⁰²(103-digit number)

24618558912307845470…89013726304504383999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.923 × 10¹⁰²(103-digit number)

49237117824615690940…78027452609008767999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.847 × 10¹⁰²(103-digit number)

98474235649231381881…56054905218017535999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.969 × 10¹⁰³(104-digit number)

19694847129846276376…12109810436035071999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.938 × 10¹⁰³(104-digit number)

39389694259692552752…24219620872070143999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.877 × 10¹⁰³(104-digit number)

78779388519385105505…48439241744140287999

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

Block #479,511

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