Block #545,694

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/15/2014, 12:21:00 PM · Difficulty 10.9541 · 6,278,957 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5e396d0d511590d882631aa87fca0ab0e0470e4d4cdd3cb222973f194c187cb7

View on Chainz ↗

Height

#545,694

Difficulty

10.954097

Transactions

Size

663 B

Version

Bits

0af43fb2

Nonce

386,915

Timestamp

5/15/2014, 12:21:00 PM

Confirmations

6,278,957

Mined by

⛏️ SaStAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d7fea1431b57af9d862cb56e2c807ab5c3b70d904bd88d9214b72fab9705e951

Transactions (1)

Coinbased7fea1431b57af…b72fab9705e951

1 in → 15 out8.3200 XPM573 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j

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.

2.443 × 10⁹⁴(95-digit number)

24431802940963753547…91264546898035302399

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

2.443 × 10⁹⁴(95-digit number)

24431802940963753547…91264546898035302399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.886 × 10⁹⁴(95-digit number)

48863605881927507094…82529093796070604799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.772 × 10⁹⁴(95-digit number)

97727211763855014189…65058187592141209599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.954 × 10⁹⁵(96-digit number)

19545442352771002837…30116375184282419199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.909 × 10⁹⁵(96-digit number)

39090884705542005675…60232750368564838399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.818 × 10⁹⁵(96-digit number)

78181769411084011351…20465500737129676799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.563 × 10⁹⁶(97-digit number)

15636353882216802270…40931001474259353599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.127 × 10⁹⁶(97-digit number)

31272707764433604540…81862002948518707199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.254 × 10⁹⁶(97-digit number)

62545415528867209081…63724005897037414399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.250 × 10⁹⁷(98-digit number)

12509083105773441816…27448011794074828799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Block #545,694

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