Block #248,280

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 7:15:45 AM · Difficulty 9.9655 · 6,550,752 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30c88a8c2291df5b76745712e70141537a200ebe786daf3441d6c30a2a1f48dd

View on Chainz ↗

Height

#248,280

Difficulty

9.965505

Transactions

Size

1.61 KB

Version

Bits

09f72b51

Nonce

4,983

Timestamp

11/7/2013, 7:15:45 AM

Confirmations

6,550,752

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

f4115173863d17cf15fb21f75a1be415c9314d8087e28d352799217f1f326312

Transactions (4)

Coinbase2f342ab05a4e19…d131d25cd13903

1 in → 2 out10.0800 XPM137 B

AZDUEbdS…RYKMRZET ASNt3cJa…L5zCqAYM

49ada97790ddb5…ab28258cfff5a0

4 in → 2 out274.9101 XPM671 B

ATP6ihBz…va7MpWW8 ASJQjSDX…bsbyrTfB

2fa4b59a01738f…99a65454c6fb71

3 in → 2 out30.1700 XPM524 B

ASHtnShU…bRJW5s3o AN7ZnJS4…uHpiPac9

1212a1a1b2a8b3…267e111d001639

1 in → 2 out3.0130 XPM225 B

APRK8Tht…8LAArKex AYY2QmEc…SzxG7b9E

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.

1.197 × 10⁹⁷(98-digit number)

11975772123649735519…49284185199845962239

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

1.197 × 10⁹⁷(98-digit number)

11975772123649735519…49284185199845962239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.197 × 10⁹⁷(98-digit number)

11975772123649735519…49284185199845962241

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

2.395 × 10⁹⁷(98-digit number)

23951544247299471039…98568370399691924479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.395 × 10⁹⁷(98-digit number)

23951544247299471039…98568370399691924481

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

4.790 × 10⁹⁷(98-digit number)

47903088494598942078…97136740799383848959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.790 × 10⁹⁷(98-digit number)

47903088494598942078…97136740799383848961

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

9.580 × 10⁹⁷(98-digit number)

95806176989197884156…94273481598767697919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.580 × 10⁹⁷(98-digit number)

95806176989197884156…94273481598767697921

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

1.916 × 10⁹⁸(99-digit number)

19161235397839576831…88546963197535395839

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