Block #439,886

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/12/2014, 12:50:34 AM · Difficulty 10.3557 · 6,355,547 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

baee124f233c8b396b0ce22ff495e2545aa7db4bbba82f9a208a2826d1ce402e

View on Chainz ↗

Height

#439,886

Difficulty

10.355676

Transactions

Size

968 B

Version

Bits

0a5b0d92

Nonce

935,754

Timestamp

3/12/2014, 12:50:34 AM

Confirmations

6,355,547

Mined by

⛏️ NoZAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

5ff8a09ce72df499f3b8da087ba6f30f5122ce762b6a519ba424f759b878271f

Transactions (1)

Coinbase5ff8a09ce72df4…24f759b878271f

1 in → 24 out9.3100 XPM879 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg Adbb4svj…dQWTHsq5 AXCBfU18…vZFjKTCm ATp4jJhs…TbSgR8Qb

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.

1.646 × 10⁹²(93-digit number)

16468783287051607601…63952801521580723039

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

1.646 × 10⁹²(93-digit number)

16468783287051607601…63952801521580723039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.293 × 10⁹²(93-digit number)

32937566574103215203…27905603043161446079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.587 × 10⁹²(93-digit number)

65875133148206430406…55811206086322892159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.317 × 10⁹³(94-digit number)

13175026629641286081…11622412172645784319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.635 × 10⁹³(94-digit number)

26350053259282572162…23244824345291568639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.270 × 10⁹³(94-digit number)

52700106518565144324…46489648690583137279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.054 × 10⁹⁴(95-digit number)

10540021303713028864…92979297381166274559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.108 × 10⁹⁴(95-digit number)

21080042607426057729…85958594762332549119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.216 × 10⁹⁴(95-digit number)

42160085214852115459…71917189524665098239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.432 × 10⁹⁴(95-digit number)

84320170429704230919…43834379049330196479

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