Block #447,376

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 6:19:03 AM · Difficulty 10.3545 · 6,359,647 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1908e0da9e85e452aabb07d1f86b35eac96cb302a21b8361dce0971c7861e978

Height

#447,376

Difficulty

10.354466

Transactions

1

Size

1004 B

Version

2

Bits

0a5abe4d

Nonce

378,393

Timestamp

3/17/2014, 6:19:03 AM

Confirmations

6,359,647

Merkle Root

9a6ff08fb06d5ef45e192873efa8bb11ef3f4d22414f82425e359dfa00f63935
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.

7.522 × 10⁹⁶(97-digit number)
75220725445483274259…95495612435851027839
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.

1
origin − 1
7.522 × 10⁹⁶(97-digit number)
75220725445483274259…95495612435851027839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.504 × 10⁹⁷(98-digit number)
15044145089096654851…90991224871702055679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.008 × 10⁹⁷(98-digit number)
30088290178193309703…81982449743404111359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.017 × 10⁹⁷(98-digit number)
60176580356386619407…63964899486808222719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.203 × 10⁹⁸(99-digit number)
12035316071277323881…27929798973616445439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.407 × 10⁹⁸(99-digit number)
24070632142554647763…55859597947232890879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.814 × 10⁹⁸(99-digit number)
48141264285109295526…11719195894465781759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.628 × 10⁹⁸(99-digit number)
96282528570218591052…23438391788931563519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.925 × 10⁹⁹(100-digit number)
19256505714043718210…46876783577863127039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.851 × 10⁹⁹(100-digit number)
38513011428087436421…93753567155726254079
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, …
Circulating Supply:57,700,286 XPM·at block #6,807,022 · updates every 60s
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