Block #244,173

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 5:12:48 PM · Difficulty 9.9626 · 6,547,742 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d209eb2f7599c0ba8cc1ccd2b80cd487adae092d77efbb9b78e37842aa4ab9e

View on Chainz ↗

Height

#244,173

Difficulty

9.962603

Transactions

Size

1.91 KB

Version

Bits

09f66d28

Nonce

3,359

Timestamp

11/4/2013, 5:12:48 PM

Confirmations

6,547,742

Merkle Root

018c18dcca8844257548990952da22abf5204b23e4b8706b0a9ba5cb0e3e8ba8

Transactions (5)

Coinbase7ad8eda734f8b3…f6442bfb3ab59b

1 in → 1 out10.1006 XPM109 B

Ab39sMrx…3VPUUQnb

34f86d6142351a…12bcc49555f8a7

2 in → 2 out12.9699 XPM372 B

ASuoUi24…FwBoFbxd AYjC9vjW…LJfmGzj3

1711c2fa188fe9…4b0d57fc12122e

3 in → 1 out6.0027 XPM489 B

AepBuXhC…nuU7jDvn

3170d2b86bb248…011eb12f520301

4 in → 4 out10.2724 XPM705 B

AHhhdQ38…J6Q51SAk AcADmAoe…8iNnoMzB AUfa5LFJ…C4BhhWGa AeKNrjNj…1NEq95Ta

da186d59786933…5b5f6af9ade367

1 in → 1 out0.0900 XPM192 B

ALay3fW3…uH61PPTg

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.

1.280 × 10⁹⁵(96-digit number)

12809423786820437430…53690791282142195849

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

1.280 × 10⁹⁵(96-digit number)

12809423786820437430…53690791282142195849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.280 × 10⁹⁵(96-digit number)

12809423786820437430…53690791282142195851

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

2.561 × 10⁹⁵(96-digit number)

25618847573640874860…07381582564284391699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.561 × 10⁹⁵(96-digit number)

25618847573640874860…07381582564284391701

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

5.123 × 10⁹⁵(96-digit number)

51237695147281749720…14763165128568783399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.123 × 10⁹⁵(96-digit number)

51237695147281749720…14763165128568783401

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

1.024 × 10⁹⁶(97-digit number)

10247539029456349944…29526330257137566799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.024 × 10⁹⁶(97-digit number)

10247539029456349944…29526330257137566801

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

2.049 × 10⁹⁶(97-digit number)

20495078058912699888…59052660514275133599

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