Block #83,720

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 8:28:34 AM · Difficulty 9.2690 · 6,707,220 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

acd619f79a8888cb32fc9b26a7e694f2b8bc1ecabadc2cce36134242ae24aa5f

View on Chainz ↗

Height

#83,720

Difficulty

9.269011

Transactions

Size

2.61 KB

Version

Bits

0944dde7

Nonce

307,686

Timestamp

7/26/2013, 8:28:34 AM

Confirmations

6,707,220

Merkle Root

5f5e7c5742bb20bbf21e4ff47e1c458e0bd5d94f120b91e5aac9c552ecd3556e

Transactions (3)

Coinbaseea071e51ac48c6…ae27554d008039

1 in → 1 out11.6600 XPM109 B

AVpW62a9…5PsHTFbw

20988ee30cba8e…c951c46d11ca68

9 in → 2 out105.1700 XPM1.07 KB

Ac3AUHow…hYeSm7Mw AJc7ETo3…y5s7mhvH

0123c5b301b610…39be7f5e7fc37b

9 in → 1 out9.8200 XPM1.34 KB

AJ68CdDX…Jc9wKXns

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.

6.690 × 10¹⁰⁶(107-digit number)

66903127663870947681…73306872440775788399

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

6.690 × 10¹⁰⁶(107-digit number)

66903127663870947681…73306872440775788399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.338 × 10¹⁰⁷(108-digit number)

13380625532774189536…46613744881551576799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.676 × 10¹⁰⁷(108-digit number)

26761251065548379072…93227489763103153599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.352 × 10¹⁰⁷(108-digit number)

53522502131096758144…86454979526206307199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.070 × 10¹⁰⁸(109-digit number)

10704500426219351628…72909959052412614399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.140 × 10¹⁰⁸(109-digit number)

21409000852438703257…45819918104825228799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.281 × 10¹⁰⁸(109-digit number)

42818001704877406515…91639836209650457599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.563 × 10¹⁰⁸(109-digit number)

85636003409754813031…83279672419300915199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.712 × 10¹⁰⁹(110-digit number)

17127200681950962606…66559344838601830399

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