Block #88,008

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/29/2013, 7:27:28 AM · Difficulty 9.2687 · 6,701,961 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

37438c1f094c550815de929b78fff4628f5fc482c91b0e848f7a2e43f311a59a

View on Chainz ↗

Height

#88,008

Difficulty

9.268704

Transactions

Size

356 B

Version

Bits

0944c9ca

Nonce

484,852

Timestamp

7/29/2013, 7:27:28 AM

Confirmations

6,701,961

Merkle Root

366f90f10f85cac08c1c3b65e234f8094bb9c938a4aeac2e132da7b79d898689

Transactions (2)

Coinbase6ed890191f4e8f…f3aecd6760b90d

1 in → 1 out11.6300 XPM109 B

AV5dwS8H…STSs4dVT

3c674bc45e2865…7be442d13e1605

1 in → 1 out12.1300 XPM158 B

ARAkqdLQ…SQugeNMr

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.

2.926 × 10⁹³(94-digit number)

29266732373721613540…84389217723279580499

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

2.926 × 10⁹³(94-digit number)

29266732373721613540…84389217723279580499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.853 × 10⁹³(94-digit number)

58533464747443227081…68778435446559160999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.170 × 10⁹⁴(95-digit number)

11706692949488645416…37556870893118321999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.341 × 10⁹⁴(95-digit number)

23413385898977290832…75113741786236643999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.682 × 10⁹⁴(95-digit number)

46826771797954581665…50227483572473287999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.365 × 10⁹⁴(95-digit number)

93653543595909163330…00454967144946575999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.873 × 10⁹⁵(96-digit number)

18730708719181832666…00909934289893151999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.746 × 10⁹⁵(96-digit number)

37461417438363665332…01819868579786303999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.492 × 10⁹⁵(96-digit number)

74922834876727330664…03639737159572607999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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