Block #526,258

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/5/2014, 6:50:39 AM · Difficulty 10.8820 · 6,300,738 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d0369c0d1bc1033d247d3044c0b9a7cff75f64ae945b482886aad3969a3bf084

View on Chainz ↗

Height

#526,258

Difficulty

10.882022

Transactions

Size

209 B

Version

Bits

0ae1cc37

Nonce

50,122,586

Timestamp

5/5/2014, 6:50:39 AM

Confirmations

6,300,738

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

65e6c0444c397a2d65f1cda20ac736cd61250ef4fb5f46368dae927c5cdf2af0

Transactions (1)

Coinbase65e6c0444c397a…ae927c5cdf2af0

1 in → 1 out8.4300 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.

1.199 × 10¹⁰¹(102-digit number)

11991360102373385172…93089697440133939199

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

1.199 × 10¹⁰¹(102-digit number)

11991360102373385172…93089697440133939199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.398 × 10¹⁰¹(102-digit number)

23982720204746770344…86179394880267878399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.796 × 10¹⁰¹(102-digit number)

47965440409493540689…72358789760535756799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.593 × 10¹⁰¹(102-digit number)

95930880818987081378…44717579521071513599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.918 × 10¹⁰²(103-digit number)

19186176163797416275…89435159042143027199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.837 × 10¹⁰²(103-digit number)

38372352327594832551…78870318084286054399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.674 × 10¹⁰²(103-digit number)

76744704655189665102…57740636168572108799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.534 × 10¹⁰³(104-digit number)

15348940931037933020…15481272337144217599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.069 × 10¹⁰³(104-digit number)

30697881862075866040…30962544674288435199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.139 × 10¹⁰³(104-digit number)

61395763724151732081…61925089348576870399

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 #526,258

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