Block #76,523

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2013, 1:27:26 AM · Difficulty 9.1046 · 6,713,413 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2f513b8675e77595b084b5285303333c485f7d932110699df1d0b98788c2260b

View on Chainz ↗

Height

#76,523

Difficulty

9.104628

Transactions

Size

203 B

Version

Bits

091ac8e5

Nonce

265

Timestamp

7/22/2013, 1:27:26 AM

Confirmations

6,713,413

Merkle Root

9e16308e4ef9d588ff634df3e3fbb5fdacefe22289b27268136e3c833bd83540

Transactions (1)

Coinbase9e16308e4ef9d5…6e3c833bd83540

1 in → 1 out12.0500 XPM110 B

AK1JUKWL…oPR4rN5o

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.

1.425 × 10¹⁰³(104-digit number)

14258039128537039395…16080880820768211749

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

1.425 × 10¹⁰³(104-digit number)

14258039128537039395…16080880820768211749

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.851 × 10¹⁰³(104-digit number)

28516078257074078791…32161761641536423499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.703 × 10¹⁰³(104-digit number)

57032156514148157583…64323523283072846999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.140 × 10¹⁰⁴(105-digit number)

11406431302829631516…28647046566145693999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.281 × 10¹⁰⁴(105-digit number)

22812862605659263033…57294093132291387999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.562 × 10¹⁰⁴(105-digit number)

45625725211318526067…14588186264582775999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.125 × 10¹⁰⁴(105-digit number)

91251450422637052134…29176372529165551999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.825 × 10¹⁰⁵(106-digit number)

18250290084527410426…58352745058331103999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.650 × 10¹⁰⁵(106-digit number)

36500580169054820853…16705490116662207999

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