Block #253,438

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 3:44:02 AM · Difficulty 9.9722 · 6,546,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acc6bc645dbcf3c24283d28e59633772bd5b68e33306d5c467c95c10f886489c

View on Chainz ↗

Height

#253,438

Difficulty

9.972161

Transactions

Size

978 B

Version

Bits

09f8df90

Nonce

668

Timestamp

11/10/2013, 3:44:02 AM

Confirmations

6,546,920

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

886e694eceb9b738e7189fce25afa9ac137812f8e4af91a870ecbdfc7774ac76

Transactions (3)

Coinbase1dc285bbfe7829…f85aba65f368e0

1 in → 2 out10.0600 XPM141 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

8d936687eb15b0…805d18b7fcb7cd

1 in → 2 out3.6655 XPM226 B

AQAwXriJ…UHZbfTWn AWeQSjL2…5Rb5v9y3

6329d32cb3a3de…d23a84fb832b0f

3 in → 2 out2.0183 XPM520 B

AbsHuT8a…DeTkowWA AUQhagDq…MuvyzGvh

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.

2.498 × 10⁹⁶(97-digit number)

24989036331712785347…06492433094667221759

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

2.498 × 10⁹⁶(97-digit number)

24989036331712785347…06492433094667221759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.498 × 10⁹⁶(97-digit number)

24989036331712785347…06492433094667221761

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

4.997 × 10⁹⁶(97-digit number)

49978072663425570695…12984866189334443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.997 × 10⁹⁶(97-digit number)

49978072663425570695…12984866189334443521

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

9.995 × 10⁹⁶(97-digit number)

99956145326851141390…25969732378668887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.995 × 10⁹⁶(97-digit number)

99956145326851141390…25969732378668887041

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

1.999 × 10⁹⁷(98-digit number)

19991229065370228278…51939464757337774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.999 × 10⁹⁷(98-digit number)

19991229065370228278…51939464757337774081

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

3.998 × 10⁹⁷(98-digit number)

39982458130740456556…03878929514675548159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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