Block #278,972

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 4:45:39 AM · Difficulty 9.9704 · 6,515,829 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a739b9b79822f18252ee944716e1c2160741f36038e8e771999dca66c22f2bea

View on Chainz ↗

Height

#278,972

Difficulty

9.970372

Transactions

Size

1.15 KB

Version

Bits

09f86a48

Nonce

35,594

Timestamp

11/28/2013, 4:45:39 AM

Confirmations

6,515,829

Mined by

⛏️ AaRrAbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

c3a204f37f43de71adcd4393db379d06da830b07e4a60f0fce4a79ef2777e743

Transactions (1)

Coinbasec3a204f37f43de…4a79ef2777e743

1 in → 30 out10.0200 XPM1.06 KB

AbtgNzNb…9Atvu81w AScAzqGc…BZ6tV1vJ Ad9pSzHt…cpJ3y2zz AUQHP8oJ…LpEKyRph APgWZwJ2…1nTrECFn

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.

2.382 × 10⁹⁴(95-digit number)

23828169671504301968…88318464366638909439

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

2.382 × 10⁹⁴(95-digit number)

23828169671504301968…88318464366638909439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.765 × 10⁹⁴(95-digit number)

47656339343008603937…76636928733277818879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.531 × 10⁹⁴(95-digit number)

95312678686017207875…53273857466555637759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.906 × 10⁹⁵(96-digit number)

19062535737203441575…06547714933111275519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.812 × 10⁹⁵(96-digit number)

38125071474406883150…13095429866222551039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.625 × 10⁹⁵(96-digit number)

76250142948813766300…26190859732445102079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.525 × 10⁹⁶(97-digit number)

15250028589762753260…52381719464890204159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.050 × 10⁹⁶(97-digit number)

30500057179525506520…04763438929780408319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.100 × 10⁹⁶(97-digit number)

61000114359051013040…09526877859560816639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.220 × 10⁹⁷(98-digit number)

12200022871810202608…19053755719121633279

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