Block #388,967

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 4:59:50 AM · Difficulty 10.4136 · 6,437,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4805ba52d8dd602b22de724be819edc31de97e553d432e7ead0cf323c19c510a

View on Chainz ↗

Height

#388,967

Difficulty

10.413626

Transactions

Size

837 B

Version

Bits

0a69e368

Nonce

175,150

Timestamp

2/4/2014, 4:59:50 AM

Confirmations

6,437,918

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

49d528487ce9982a9d1a3672827aadf9e725e390b735ea92d6fc6d680c9417c6

Transactions (3)

Coinbaseb812b73c220a40…970737c507e3cf

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

25a902743665ea…abc2db28b3359b

2 in → 3 out104.1306 XPM409 B

AaY3TrYd…FpEg6ghH AGbdtniR…TiNNX5xe AYZ8eYM5…LJC5y45q

5d37e4f348bf60…6a2053587a8663

1 in → 2 out1.1248 XPM227 B

AbeRsLta…bkdmYkAH Ad8EJR9M…HsM7myDg

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.

2.248 × 10⁹⁷(98-digit number)

22481832530536856568…39774180693568142079

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

2.248 × 10⁹⁷(98-digit number)

22481832530536856568…39774180693568142079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.248 × 10⁹⁷(98-digit number)

22481832530536856568…39774180693568142081

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

4.496 × 10⁹⁷(98-digit number)

44963665061073713137…79548361387136284159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.496 × 10⁹⁷(98-digit number)

44963665061073713137…79548361387136284161

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

8.992 × 10⁹⁷(98-digit number)

89927330122147426274…59096722774272568319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.992 × 10⁹⁷(98-digit number)

89927330122147426274…59096722774272568321

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

1.798 × 10⁹⁸(99-digit number)

17985466024429485254…18193445548545136639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.798 × 10⁹⁸(99-digit number)

17985466024429485254…18193445548545136641

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

3.597 × 10⁹⁸(99-digit number)

35970932048858970509…36386891097090273279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.597 × 10⁹⁸(99-digit number)

35970932048858970509…36386891097090273281

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #388,967

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