Block #497,210

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/17/2014, 11:45:47 AM · Difficulty 10.7644 · 6,307,006 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f8dd06412d19a981fd5384fd94d0768faa375724a6fa3a1e42b8e77946785d67

View on Chainz ↗

Height

#497,210

Difficulty

10.764372

Transactions

Size

549 B

Version

Bits

0ac3addc

Nonce

65,999,339

Timestamp

4/17/2014, 11:45:47 AM

Confirmations

6,307,006

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4efd76b5dc80fc66ae6f0d3031dce545a1031c73654aca3905cfd152289bc912

Transactions (2)

Coinbase43f80dd51a07f8…4c1e9d409929fc

1 in → 1 out8.6375 XPM116 B

AbwWkWZt…kawDhufa

940672196acd9d…db3e77e050cd79

2 in → 1 out4.0000 XPM341 B

AWAvCVrL…Bj3MDR7s

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.

2.380 × 10⁹⁹(100-digit number)

23803607159903465377…39372727403719674879

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

2.380 × 10⁹⁹(100-digit number)

23803607159903465377…39372727403719674879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.760 × 10⁹⁹(100-digit number)

47607214319806930755…78745454807439349759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.521 × 10⁹⁹(100-digit number)

95214428639613861511…57490909614878699519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.904 × 10¹⁰⁰(101-digit number)

19042885727922772302…14981819229757399039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.808 × 10¹⁰⁰(101-digit number)

38085771455845544604…29963638459514798079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.617 × 10¹⁰⁰(101-digit number)

76171542911691089209…59927276919029596159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.523 × 10¹⁰¹(102-digit number)

15234308582338217841…19854553838059192319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.046 × 10¹⁰¹(102-digit number)

30468617164676435683…39709107676118384639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.093 × 10¹⁰¹(102-digit number)

60937234329352871367…79418215352236769279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.218 × 10¹⁰²(103-digit number)

12187446865870574273…58836430704473538559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.437 × 10¹⁰²(103-digit number)

24374893731741148547…17672861408947077119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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