Block #61,520

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 1:48:25 PM · Difficulty 8.9734 · 6,737,838 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1fad793dfdeba92dc226a8a78d8cab8f6558dd2da1f8c2c52a65b8339b720421

View on Chainz ↗

Height

#61,520

Difficulty

8.973404

Transactions

Size

201 B

Version

Bits

08f93108

Nonce

200

Timestamp

7/18/2013, 1:48:25 PM

Confirmations

6,737,838

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

5261fe3f2c484190927039066def3b52860e96bf25a1ef46815f3b1520378dd2

Transactions (1)

Coinbase5261fe3f2c4841…5f3b1520378dd2

1 in → 1 out12.4000 XPM109 B

AV3Mx3Aq…AKiwER2W

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.

4.834 × 10⁹⁹(100-digit number)

48349357156834966871…26684073781686027659

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

4.834 × 10⁹⁹(100-digit number)

48349357156834966871…26684073781686027659

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.669 × 10⁹⁹(100-digit number)

96698714313669933743…53368147563372055319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.933 × 10¹⁰⁰(101-digit number)

19339742862733986748…06736295126744110639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.867 × 10¹⁰⁰(101-digit number)

38679485725467973497…13472590253488221279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.735 × 10¹⁰⁰(101-digit number)

77358971450935946994…26945180506976442559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.547 × 10¹⁰¹(102-digit number)

15471794290187189398…53890361013952885119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.094 × 10¹⁰¹(102-digit number)

30943588580374378797…07780722027905770239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.188 × 10¹⁰¹(102-digit number)

61887177160748757595…15561444055811540479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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