Block #74,568

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 11:48:57 AM · Difficulty 8.9956 · 6,720,072 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8983ca476effc5cb15692cab1391779d7c8f0bd60131a7fa49c99beb3830652b

View on Chainz ↗

Height

#74,568

Difficulty

8.995589

Transactions

Size

201 B

Version

Bits

08fedeea

Nonce

Timestamp

7/21/2013, 11:48:57 AM

Confirmations

6,720,072

Mined by

⛏️ P2SHAVQxbFsH6aZpX2pFKM69EEQVEFKG2vYXbz

Merkle Root

214453cc1530c18511e9e1ab3076b2c0d63d09e12e9b112ec02f349cbb15d623

Transactions (1)

Coinbase214453cc1530c1…2f349cbb15d623

1 in → 1 out12.3400 XPM109 B

AVQxbFsH…KG2vYXbz

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.

3.416 × 10⁹⁹(100-digit number)

34162222611945816921…58087986072326883299

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

3.416 × 10⁹⁹(100-digit number)

34162222611945816921…58087986072326883299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.832 × 10⁹⁹(100-digit number)

68324445223891633842…16175972144653766599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.366 × 10¹⁰⁰(101-digit number)

13664889044778326768…32351944289307533199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.732 × 10¹⁰⁰(101-digit number)

27329778089556653537…64703888578615066399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.465 × 10¹⁰⁰(101-digit number)

54659556179113307074…29407777157230132799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.093 × 10¹⁰¹(102-digit number)

10931911235822661414…58815554314460265599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.186 × 10¹⁰¹(102-digit number)

21863822471645322829…17631108628920531199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.372 × 10¹⁰¹(102-digit number)

43727644943290645659…35262217257841062399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.745 × 10¹⁰¹(102-digit number)

87455289886581291318…70524434515682124799

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