Block #427,427

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/3/2014, 9:01:02 AM · Difficulty 10.3488 · 6,371,493 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2fc71a2cbb2151ad355249429dce1c5cd3ac3583138d277120fdaa3a2dbf232a

View on Chainz ↗

Height

#427,427

Difficulty

10.348800

Transactions

Size

1.01 KB

Version

Bits

0a594af9

Nonce

16,383

Timestamp

3/3/2014, 9:01:02 AM

Confirmations

6,371,493

Mined by

⛏️ aSDAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

b29a23fef6cac67e8a785208bea202de43dcfbc00b49d5fda26a6fc72e2f6584

Transactions (1)

Coinbaseb29a23fef6cac6…6a6fc72e2f6584

1 in → 26 out9.3200 XPM947 B

AFutDVqJ…TJTJj6UF AZWiC56x…NwextJca Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

6.377 × 10⁸⁸(89-digit number)

63774919194382952634…33164164773675074549

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

6.377 × 10⁸⁸(89-digit number)

63774919194382952634…33164164773675074549

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.275 × 10⁸⁹(90-digit number)

12754983838876590526…66328329547350149099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.550 × 10⁸⁹(90-digit number)

25509967677753181053…32656659094700298199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.101 × 10⁸⁹(90-digit number)

51019935355506362107…65313318189400596399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.020 × 10⁹⁰(91-digit number)

10203987071101272421…30626636378801192799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.040 × 10⁹⁰(91-digit number)

20407974142202544843…61253272757602385599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.081 × 10⁹⁰(91-digit number)

40815948284405089686…22506545515204771199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.163 × 10⁹⁰(91-digit number)

81631896568810179372…45013091030409542399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.632 × 10⁹¹(92-digit number)

16326379313762035874…90026182060819084799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.265 × 10⁹¹(92-digit number)

32652758627524071748…80052364121638169599

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