Block #26,496

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/13/2013, 5:35:31 AM · Difficulty 7.9754 · 6,766,838 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f36de101e5dcad098f78ffa4cebfef5b8fd60586efe30907149596d768070153

View on Chainz ↗

Height

#26,496

Difficulty

7.975396

Transactions

Size

1.00 KB

Version

Bits

07f9b38c

Nonce

862

Timestamp

7/13/2013, 5:35:31 AM

Confirmations

6,766,838

Merkle Root

023f42247ee4872e62e2837d3039576385367decaa5c0b05096b486f65f9e0c4

Transactions (2)

Coinbasefd68ab92f1cfc6…c6cfa2f16a7449

1 in → 1 out15.7100 XPM109 B

AMVet1UE…hBQptM5k

f82792d4125597…4d14115ea47d97

6 in → 1 out47.3700 XPM828 B

AMmUy3x3…qPezWtyV

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.

2.200 × 10⁹³(94-digit number)

22004858903567481464…34219467081035235789

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

2.200 × 10⁹³(94-digit number)

22004858903567481464…34219467081035235789

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.400 × 10⁹³(94-digit number)

44009717807134962929…68438934162070471579

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.801 × 10⁹³(94-digit number)

88019435614269925858…36877868324140943159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.760 × 10⁹⁴(95-digit number)

17603887122853985171…73755736648281886319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.520 × 10⁹⁴(95-digit number)

35207774245707970343…47511473296563772639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.041 × 10⁹⁴(95-digit number)

70415548491415940686…95022946593127545279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.408 × 10⁹⁵(96-digit number)

14083109698283188137…90045893186255090559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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