Block #305,017

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 6:12:25 AM · Difficulty 9.9935 · 6,497,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

47e565b1babf7b7b25e70cb915af4d90e5aab06d60a02e6572306c9c4c8c0122

View on Chainz ↗

Height

#305,017

Difficulty

9.993495

Transactions

Size

2.09 KB

Version

Bits

09fe55b8

Nonce

278,624

Timestamp

12/11/2013, 6:12:25 AM

Confirmations

6,497,686

Mined by

⛏️ yaRARcqMJhpYZE2kngc2mc4PFnwnaRVLToQ6S

Merkle Root

59d0f6f2770ee1bac6b317b87fc1492519ebbefeed419ca80ea1d2b492e4ec11

Transactions (2)

Coinbase17ce11f18cc20b…0f4ccd9549089d

1 in → 30 out9.9800 XPM1.06 KB

ARcqMJhp…RVLToQ6S AG5YAjec…VhA4Aeh1 AKwqFUdz…D4jGNKFN Aex6BWoP…k2gekohW AdwvoZJ4…h9vVTWnh

215d17585e27df…46086270fa35f3

6 in → 2 out6.1269 XPM966 B

AJJGJJf7…VPzWURcx AaM2de4j…4AbXawpL

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.

2.476 × 10⁹⁰(91-digit number)

24768776087640444734…08908166097064311759

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

2.476 × 10⁹⁰(91-digit number)

24768776087640444734…08908166097064311759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.476 × 10⁹⁰(91-digit number)

24768776087640444734…08908166097064311761

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

4.953 × 10⁹⁰(91-digit number)

49537552175280889468…17816332194128623519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.953 × 10⁹⁰(91-digit number)

49537552175280889468…17816332194128623521

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

9.907 × 10⁹⁰(91-digit number)

99075104350561778937…35632664388257247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.907 × 10⁹⁰(91-digit number)

99075104350561778937…35632664388257247041

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

1.981 × 10⁹¹(92-digit number)

19815020870112355787…71265328776514494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.981 × 10⁹¹(92-digit number)

19815020870112355787…71265328776514494081

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

3.963 × 10⁹¹(92-digit number)

39630041740224711575…42530657553028988159

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