Block #254,229

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 2:35:39 PM · Difficulty 9.9729 · 6,549,082 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c077a83dfe2d9dcd49692df58e287eb4dcccccaee4bb1441cf7904b4da779149

View on Chainz ↗

Height

#254,229

Difficulty

9.972938

Transactions

Size

1.79 KB

Version

Bits

09f91277

Nonce

5,232

Timestamp

11/10/2013, 2:35:39 PM

Confirmations

6,549,082

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

56c60ff54ca0bf055bbb45432deb245b9f672dc16b740f0e16aaa6f3d14f6655

Transactions (3)

Coinbase2382977899723e…9b79f9f90c8a95

1 in → 2 out10.0700 XPM141 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

5c188b7a819fe2…b35da0606ad600

2 in → 1 out94.5000 XPM339 B

AKwrbUyw…r8ueWobo

b8f0876e015ff8…c9d5feda5447fb

8 in → 2 out3.0208 XPM1.23 KB

AUi56htg…pf8nicRC AeKNrjNj…1NEq95Ta

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.

2.787 × 10⁹⁶(97-digit number)

27875621452208071396…62452809906216817759

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

2.787 × 10⁹⁶(97-digit number)

27875621452208071396…62452809906216817759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.787 × 10⁹⁶(97-digit number)

27875621452208071396…62452809906216817761

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

5.575 × 10⁹⁶(97-digit number)

55751242904416142792…24905619812433635519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.575 × 10⁹⁶(97-digit number)

55751242904416142792…24905619812433635521

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

1.115 × 10⁹⁷(98-digit number)

11150248580883228558…49811239624867271039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.115 × 10⁹⁷(98-digit number)

11150248580883228558…49811239624867271041

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

2.230 × 10⁹⁷(98-digit number)

22300497161766457116…99622479249734542079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.230 × 10⁹⁷(98-digit number)

22300497161766457116…99622479249734542081

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

4.460 × 10⁹⁷(98-digit number)

44600994323532914233…99244958499469084159

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