Block #71,769

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 8:22:08 PM · Difficulty 8.9935 · 6,719,544 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

81c44e476322cddbd4bd756c27c978d60c70299531eb13f7f1bb7fd2c0c84bbf

View on Chainz ↗

Height

#71,769

Difficulty

8.993504

Transactions

Size

360 B

Version

Bits

08fe5643

Nonce

Timestamp

7/20/2013, 8:22:08 PM

Confirmations

6,719,544

Merkle Root

7c1639c230649862aee76da7a801601044132c6570e65a2e76501c2153b3fec1

Transactions (2)

Coinbase9c605fa945b1a9…71f9c020a08d82

1 in → 1 out12.3600 XPM110 B

AXSFye4r…ADf1YWCU

79f1b92eac13e8…d39faf726aba01

1 in → 1 out12.3500 XPM159 B

AG7dvNsQ…8mYEdta9

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.

3.551 × 10⁹⁷(98-digit number)

35513391736873322080…90394411319296787439

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

3.551 × 10⁹⁷(98-digit number)

35513391736873322080…90394411319296787439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.102 × 10⁹⁷(98-digit number)

71026783473746644161…80788822638593574879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.420 × 10⁹⁸(99-digit number)

14205356694749328832…61577645277187149759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.841 × 10⁹⁸(99-digit number)

28410713389498657664…23155290554374299519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.682 × 10⁹⁸(99-digit number)

56821426778997315328…46310581108748599039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.136 × 10⁹⁹(100-digit number)

11364285355799463065…92621162217497198079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.272 × 10⁹⁹(100-digit number)

22728570711598926131…85242324434994396159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.545 × 10⁹⁹(100-digit number)

45457141423197852263…70484648869988792319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.091 × 10⁹⁹(100-digit number)

90914282846395704526…40969297739977584639

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