Block #464,398

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 6:25:33 PM · Difficulty 10.4208 · 6,332,420 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ab978fbde78bf72003dff46d3944b34ba9fef77bf393ae67eb82efe90cb4f09

View on Chainz ↗

Height

#464,398

Difficulty

10.420826

Transactions

Size

209 B

Version

Bits

0a6bbb47

Nonce

1,760

Timestamp

3/28/2014, 6:25:33 PM

Confirmations

6,332,420

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3bd55776d3d8ca30263f81f72b5362c70e512d8d769d26cff05be8e3bf79589d

Transactions (1)

Coinbase3bd55776d3d8ca…5be8e3bf79589d

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

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.

4.294 × 10¹⁰⁰(101-digit number)

42943338080915637503…66337357340117066239

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

4.294 × 10¹⁰⁰(101-digit number)

42943338080915637503…66337357340117066239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.294 × 10¹⁰⁰(101-digit number)

42943338080915637503…66337357340117066241

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

8.588 × 10¹⁰⁰(101-digit number)

85886676161831275006…32674714680234132479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.588 × 10¹⁰⁰(101-digit number)

85886676161831275006…32674714680234132481

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

1.717 × 10¹⁰¹(102-digit number)

17177335232366255001…65349429360468264959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.717 × 10¹⁰¹(102-digit number)

17177335232366255001…65349429360468264961

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

3.435 × 10¹⁰¹(102-digit number)

34354670464732510002…30698858720936529919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.435 × 10¹⁰¹(102-digit number)

34354670464732510002…30698858720936529921

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

6.870 × 10¹⁰¹(102-digit number)

68709340929465020005…61397717441873059839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.870 × 10¹⁰¹(102-digit number)

68709340929465020005…61397717441873059841

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