Block #88,756

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/29/2013, 8:48:39 PM · Difficulty 9.2657 · 6,710,597 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

dc6a591ef306e866fe7130fbb22986dfc2266fc274b0b5cd1136badafebdd330

View on Chainz ↗

Height

#88,756

Difficulty

9.265707

Transactions

Size

202 B

Version

Bits

09440560

Nonce

271

Timestamp

7/29/2013, 8:48:39 PM

Confirmations

6,710,597

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

23b210b7b7d3964ae624ff61d4fa0fc6fcf027ba1bc3b7c5e8cb17420a675f87

Transactions (1)

Coinbase23b210b7b7d396…cb17420a675f87

1 in → 1 out11.6300 XPM109 B

AcuJraLT…Y66BS47Q

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.

6.807 × 10¹⁰²(103-digit number)

68077898266743360800…59690078406702725389

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

6.807 × 10¹⁰²(103-digit number)

68077898266743360800…59690078406702725389

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.361 × 10¹⁰³(104-digit number)

13615579653348672160…19380156813405450779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.723 × 10¹⁰³(104-digit number)

27231159306697344320…38760313626810901559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.446 × 10¹⁰³(104-digit number)

54462318613394688640…77520627253621803119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.089 × 10¹⁰⁴(105-digit number)

10892463722678937728…55041254507243606239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.178 × 10¹⁰⁴(105-digit number)

21784927445357875456…10082509014487212479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.356 × 10¹⁰⁴(105-digit number)

43569854890715750912…20165018028974424959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.713 × 10¹⁰⁴(105-digit number)

87139709781431501824…40330036057948849919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.742 × 10¹⁰⁵(106-digit number)

17427941956286300364…80660072115897699839

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