Block #300,452

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 2:27:58 PM · Difficulty 9.9923 · 6,511,984 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

f72b5275932d21e9759de52d83c0b2693070dec085068b749bc401cf3491e98e

View on Chainz ↗

Height

#300,452

Difficulty

9.992303

Transactions

Size

1.14 KB

Version

Bits

09fe0793

Nonce

157,084

Timestamp

12/8/2013, 2:27:58 PM

Confirmations

6,511,984

Mined by

⛏️ aR5ASWX42VMMDPu9AeW1CGnoamzT3XypQABkY

Merkle Root

9808b0983486e8d5a35aeba19bfc95a62803c41c7721f540a459c23087869c0c

Transactions (1)

Coinbase9808b0983486e8…59c23087869c0c

1 in → 30 out9.9800 XPM1.06 KB

ASWX42VM…XypQABkY AZ2pPuKg…95SN2Yr7 Acs9SHrk…QJSB8SFG AWA5FEzr…x9RdPKTy AHjxjypg…BfqPH2LH

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.

3.301 × 10⁹¹(92-digit number)

33014189073243553822…17942174566783745279

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 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.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.301 × 10⁹¹(92-digit number)

33014189073243553822…17942174566783745279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.301 × 10⁹¹(92-digit number)

33014189073243553822…17942174566783745281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.602 × 10⁹¹(92-digit number)

66028378146487107644…35884349133567490559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.602 × 10⁹¹(92-digit number)

66028378146487107644…35884349133567490561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.320 × 10⁹²(93-digit number)

13205675629297421528…71768698267134981119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.320 × 10⁹²(93-digit number)

13205675629297421528…71768698267134981121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.641 × 10⁹²(93-digit number)

26411351258594843057…43537396534269962239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.641 × 10⁹²(93-digit number)

26411351258594843057…43537396534269962241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.282 × 10⁹²(93-digit number)

52822702517189686115…87074793068539924479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.282 × 10⁹²(93-digit number)

52822702517189686115…87074793068539924481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #300,452

Cookie Preferences