Block #257,993

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/12/2013, 7:16:25 PM · Difficulty 9.9761 · 6,551,002 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

283325abd16f2b16343fc2ce87709815196dca515d7595a6c49a73c2aaa35d19

View on Chainz ↗

Height

#257,993

Difficulty

9.976107

Transactions

Size

2.04 KB

Version

Bits

09f9e220

Nonce

241,809

Timestamp

11/12/2013, 7:16:25 PM

Confirmations

6,551,002

Mined by

⛏️ aR~8AP6kEuabo393SyqjThYC3c6KVbX1oCE7Nm

Merkle Root

c297e256e9a28574d8178c8afd19f6b5c5d3209d50a9e52bfe58a3f991b75eab

Transactions (1)

Coinbasec297e256e9a285…58a3f991b75eab

1 in → 57 out10.0100 XPM1.95 KB

AP6kEuab…X1oCE7Nm ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC AQTQxLiv…s1fK2esi ARR7aRH6…ne3DXGXZ

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.

7.776 × 10⁹⁴(95-digit number)

77767486134326567743…83476255105140765759

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

7.776 × 10⁹⁴(95-digit number)

77767486134326567743…83476255105140765759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.776 × 10⁹⁴(95-digit number)

77767486134326567743…83476255105140765761

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

1.555 × 10⁹⁵(96-digit number)

15553497226865313548…66952510210281531519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.555 × 10⁹⁵(96-digit number)

15553497226865313548…66952510210281531521

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

3.110 × 10⁹⁵(96-digit number)

31106994453730627097…33905020420563063039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.110 × 10⁹⁵(96-digit number)

31106994453730627097…33905020420563063041

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

6.221 × 10⁹⁵(96-digit number)

62213988907461254194…67810040841126126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.221 × 10⁹⁵(96-digit number)

62213988907461254194…67810040841126126081

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

1.244 × 10⁹⁶(97-digit number)

12442797781492250838…35620081682252252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.244 × 10⁹⁶(97-digit number)

12442797781492250838…35620081682252252161

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.488 × 10⁹⁶(97-digit number)

24885595562984501677…71240163364504504319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #257,993

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