Block #452,528

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/20/2014, 3:42:54 PM · Difficulty 10.3905 · 6,349,601 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fb891cacbeea70c071f9b01d4f601f15bb00778d9a6ab3db6c0dd1d73999db2f

View on Chainz ↗

Height

#452,528

Difficulty

10.390529

Transactions

Size

1020 B

Version

Bits

0a63f9bd

Nonce

43,139

Timestamp

3/20/2014, 3:42:54 PM

Confirmations

6,349,601

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

97ab1013c7a1fb2769cee2c991639a14dc52231337156a6d2194ecf39088b5e1

Transactions (2)

Coinbaseec870ded05bb89…b8721947248e5b

1 in → 1 out9.2600 XPM110 B

AeKNrjNj…1NEq95Ta

e18a0c94ab1ed1…4ea5a88d6d0f2b

5 in → 2 out337.3081 XPM819 B

ATQfr7c3…u7WozS22 AJVFgj9c…tfAvds5Q

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.

7.583 × 10⁹⁵(96-digit number)

75837159411084236840…91056182325619755389

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

7.583 × 10⁹⁵(96-digit number)

75837159411084236840…91056182325619755389

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.516 × 10⁹⁶(97-digit number)

15167431882216847368…82112364651239510779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.033 × 10⁹⁶(97-digit number)

30334863764433694736…64224729302479021559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.066 × 10⁹⁶(97-digit number)

60669727528867389472…28449458604958043119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.213 × 10⁹⁷(98-digit number)

12133945505773477894…56898917209916086239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.426 × 10⁹⁷(98-digit number)

24267891011546955789…13797834419832172479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.853 × 10⁹⁷(98-digit number)

48535782023093911578…27595668839664344959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.707 × 10⁹⁷(98-digit number)

97071564046187823156…55191337679328689919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.941 × 10⁹⁸(99-digit number)

19414312809237564631…10382675358657379839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.882 × 10⁹⁸(99-digit number)

38828625618475129262…20765350717314759679

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