Block #450,551

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/19/2014, 9:09:58 AM · Difficulty 10.3722 · 6,345,446 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

092342f629984887684717e7c5f4caa00b3432f1cc25dba97bc6805e0d925d94

View on Chainz ↗

Height

#450,551

Difficulty

10.372226

Transactions

Size

1005 B

Version

Bits

0a5f4a2e

Nonce

173,886

Timestamp

3/19/2014, 9:09:58 AM

Confirmations

6,345,446

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

62aeceee13997daa0163bc275ebf03fe54159b36d105cce6f5bcd71371253707

Transactions (1)

Coinbase62aeceee13997d…bcd71371253707

1 in → 25 out9.2800 XPM913 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

9.433 × 10⁹⁹(100-digit number)

94337392454795329141…35406753168410431039

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

9.433 × 10⁹⁹(100-digit number)

94337392454795329141…35406753168410431039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.886 × 10¹⁰⁰(101-digit number)

18867478490959065828…70813506336820862079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.773 × 10¹⁰⁰(101-digit number)

37734956981918131656…41627012673641724159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.546 × 10¹⁰⁰(101-digit number)

75469913963836263313…83254025347283448319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.509 × 10¹⁰¹(102-digit number)

15093982792767252662…66508050694566896639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.018 × 10¹⁰¹(102-digit number)

30187965585534505325…33016101389133793279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.037 × 10¹⁰¹(102-digit number)

60375931171069010650…66032202778267586559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.207 × 10¹⁰²(103-digit number)

12075186234213802130…32064405556535173119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.415 × 10¹⁰²(103-digit number)

24150372468427604260…64128811113070346239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.830 × 10¹⁰²(103-digit number)

48300744936855208520…28257622226140692479

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