Block #473,694

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/4/2014, 2:26:53 AM · Difficulty 10.4456 · 6,322,402 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9933c93010728f29a5585f74ebae4acb9a58d0c670212c3ad84c75f5e590c772

View on Chainz ↗

Height

#473,694

Difficulty

10.445628

Transactions

Size

726 B

Version

Bits

0a7214a7

Nonce

59,214

Timestamp

4/4/2014, 2:26:53 AM

Confirmations

6,322,402

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fd4a5f089786f6a1c93b34f18f2079a0290efdf93bb5447196f173fbfc525aa5

Transactions (2)

Coinbase29a0e844420258…5625d54e6a402e

1 in → 1 out9.1600 XPM116 B

AbwWkWZt…kawDhufa

721ad40622a0f8…96716b4588905b

3 in → 2 out156.5788 XPM521 B

AR3NsN6L…zoMC9e95 ATepM8qV…KGFNGDwn

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.

6.408 × 10⁹²(93-digit number)

64080858170341044067…09338096745519201719

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

6.408 × 10⁹²(93-digit number)

64080858170341044067…09338096745519201719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.281 × 10⁹³(94-digit number)

12816171634068208813…18676193491038403439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.563 × 10⁹³(94-digit number)

25632343268136417626…37352386982076806879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.126 × 10⁹³(94-digit number)

51264686536272835253…74704773964153613759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.025 × 10⁹⁴(95-digit number)

10252937307254567050…49409547928307227519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.050 × 10⁹⁴(95-digit number)

20505874614509134101…98819095856614455039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.101 × 10⁹⁴(95-digit number)

41011749229018268202…97638191713228910079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.202 × 10⁹⁴(95-digit number)

82023498458036536405…95276383426457820159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.640 × 10⁹⁵(96-digit number)

16404699691607307281…90552766852915640319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.280 × 10⁹⁵(96-digit number)

32809399383214614562…81105533705831280639

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