Block #300,257

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 12:02:00 PM · Difficulty 9.9922 · 6,509,900 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53790609e21c9ecc34879c96033dfd20a8ae41308ef7933b678df50d994005bb

View on Chainz ↗

Height

#300,257

Difficulty

9.992230

Transactions

Size

1.95 KB

Version

Bits

09fe02cb

Nonce

6,259

Timestamp

12/8/2013, 12:02:00 PM

Confirmations

6,509,900

Mined by

⛏️ aR_Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

79977c0f1d8f18a83d11f2d3b390a3a27e9bd8f66c03aa0bec8069538984ba12

Transactions (4)

Coinbasecfdb50c147933e…8897b836707f7b

1 in → 31 out9.9800 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz AWA5FEzr…x9RdPKTy AN8nUzff…YcDfRDQ2 AKwcMAcH…WGekVdtp AQyr8Lw3…hs4nt3Pn

3386f929e52f8b…0011aac6dc27e7

1 in → 2 out3487.2816 XPM226 B

ANACcpQp…KTrfeZoh AG88DweJ…QeQTqESq

ae5ad743d9c027…b7362e8bfced7a

2 in → 1 out65.5800 XPM342 B

AKSxfKfu…PrY2y58U

3f14ac68582818…44e5975275f090

1 in → 2 out3437.2628 XPM226 B

ANaGkcSY…coLukWy5 AJb5HuFc…9Ts4jaVZ

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.

1.599 × 10⁹⁵(96-digit number)

15994321513823640169…43287796183624715839

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

1.599 × 10⁹⁵(96-digit number)

15994321513823640169…43287796183624715839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.599 × 10⁹⁵(96-digit number)

15994321513823640169…43287796183624715841

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

3.198 × 10⁹⁵(96-digit number)

31988643027647280338…86575592367249431679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.198 × 10⁹⁵(96-digit number)

31988643027647280338…86575592367249431681

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

6.397 × 10⁹⁵(96-digit number)

63977286055294560676…73151184734498863359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.397 × 10⁹⁵(96-digit number)

63977286055294560676…73151184734498863361

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

1.279 × 10⁹⁶(97-digit number)

12795457211058912135…46302369468997726719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.279 × 10⁹⁶(97-digit number)

12795457211058912135…46302369468997726721

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

2.559 × 10⁹⁶(97-digit number)

25590914422117824270…92604738937995453439

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

Block #300,257

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