Block #193,392

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/4/2013, 11:52:30 AM · Difficulty 9.8763 · 6,602,763 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

65dfec18a276a7954800ac1283646a02203e431d6fe7ce76932cb8b43bc04a85

View on Chainz ↗

Height

#193,392

Difficulty

9.876346

Transactions

Size

4.27 KB

Version

Bits

09e0583e

Nonce

1,164,784,207

Timestamp

10/4/2013, 11:52:30 AM

Confirmations

6,602,763

Mined by

⛏️ pRNAVW3nNAFY2E5ogLrtA27TPorCcihzUUPP1

Merkle Root

1bee010ae9757160761b785ce3da878a165c7e9b0f822fb88462c361314aea21

Transactions (1)

Coinbase1bee010ae97571…62c361314aea21

1 in → 124 out10.1900 XPM4.18 KB

AVW3nNAF…ihzUUPP1 AQTQxLiv…s1fK2esi AcKcNjCB…MZipfo4V AcNvVMY6…UfezsnjX AcKMedRX…21yGxZHx

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.

7.989 × 10⁹⁸(99-digit number)

79890931734912220729…04404201070913919999

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

7.989 × 10⁹⁸(99-digit number)

79890931734912220729…04404201070913919999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.597 × 10⁹⁹(100-digit number)

15978186346982444145…08808402141827839999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.195 × 10⁹⁹(100-digit number)

31956372693964888291…17616804283655679999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.391 × 10⁹⁹(100-digit number)

63912745387929776583…35233608567311359999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.278 × 10¹⁰⁰(101-digit number)

12782549077585955316…70467217134622719999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.556 × 10¹⁰⁰(101-digit number)

25565098155171910633…40934434269245439999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.113 × 10¹⁰⁰(101-digit number)

51130196310343821267…81868868538490879999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.022 × 10¹⁰¹(102-digit number)

10226039262068764253…63737737076981759999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.045 × 10¹⁰¹(102-digit number)

20452078524137528506…27475474153963519999

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