Block #53,202

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/16/2013, 2:11:13 PM · Difficulty 8.9210 · 6,738,216 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

195c34b1a55339fd36b17304020552f088fc5ffdd40657f500cc6ab3e84e54f9

View on Chainz ↗

Height

#53,202

Difficulty

8.920954

Transactions

Size

834 B

Version

Bits

08ebc3a2

Nonce

338

Timestamp

7/16/2013, 2:11:13 PM

Confirmations

6,738,216

Merkle Root

d2e0eebc3268713410b1fa0f6900f26dc749ee2ad76bc2c809480a262c203cd9

Transactions (2)

Coinbase90bf521d9216e4…a134684e35af44

1 in → 1 out12.5600 XPM110 B

ATy6QP7c…BXkPHx3v

db86a47d663923…7698fdfd3882cd

4 in → 1 out1250.9000 XPM637 B

Af72phx2…8eoFuBNY

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.

4.109 × 10⁸⁸(89-digit number)

41097507071970293431…11927884030145873439

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

4.109 × 10⁸⁸(89-digit number)

41097507071970293431…11927884030145873439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.219 × 10⁸⁸(89-digit number)

82195014143940586863…23855768060291746879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.643 × 10⁸⁹(90-digit number)

16439002828788117372…47711536120583493759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.287 × 10⁸⁹(90-digit number)

32878005657576234745…95423072241166987519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.575 × 10⁸⁹(90-digit number)

65756011315152469491…90846144482333975039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.315 × 10⁹⁰(91-digit number)

13151202263030493898…81692288964667950079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.630 × 10⁹⁰(91-digit number)

26302404526060987796…63384577929335900159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.260 × 10⁹⁰(91-digit number)

52604809052121975592…26769155858671800319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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