Block #93,551

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/2/2013, 12:17:10 PM · Difficulty 9.1973 · 6,697,443 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3164df389df549e34302b4c7923ecf9aa40e3f008bb9e2129661dcc30b9629e7

View on Chainz ↗

Height

#93,551

Difficulty

9.197273

Transactions

Size

1.41 KB

Version

Bits

09328075

Nonce

136,478

Timestamp

8/2/2013, 12:17:10 PM

Confirmations

6,697,443

Merkle Root

a5bf02612339c63f6236228cfe947a472aa46c6a8e40670a6096984336715909

Transactions (3)

Coinbase96a0c7d108cfc0…84995bac067569

1 in → 1 out11.8300 XPM109 B

AcBadmkp…GmhL921o

58da6f50d6f102…264bbb6f276e1b

7 in → 2 out50.0500 XPM1.05 KB

AeercaAQ…oQFySLTg AcJnSyvn…VijA5cNC

9e31e748c2a5f1…fe1ab601e1ea45

1 in → 1 out11.6500 XPM158 B

AeTde7fH…w7crTzqr

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.

1.561 × 10¹⁰⁸(109-digit number)

15610743508580337449…69345882120783310429

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

1.561 × 10¹⁰⁸(109-digit number)

15610743508580337449…69345882120783310429

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.122 × 10¹⁰⁸(109-digit number)

31221487017160674899…38691764241566620859

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.244 × 10¹⁰⁸(109-digit number)

62442974034321349798…77383528483133241719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.248 × 10¹⁰⁹(110-digit number)

12488594806864269959…54767056966266483439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.497 × 10¹⁰⁹(110-digit number)

24977189613728539919…09534113932532966879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.995 × 10¹⁰⁹(110-digit number)

49954379227457079838…19068227865065933759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.990 × 10¹⁰⁹(110-digit number)

99908758454914159677…38136455730131867519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.998 × 10¹¹⁰(111-digit number)

19981751690982831935…76272911460263735039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.996 × 10¹¹⁰(111-digit number)

39963503381965663871…52545822920527470079

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