Block #200,864

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 6:53:13 AM · Difficulty 9.8905 · 6,616,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

faa8f9920d112cd121b769dbb777a714b53abf273c6c4aa71931bcd7f8144a9e

View on Chainz ↗

Height

#200,864

Difficulty

9.890507

Transactions

Size

35.55 KB

Version

Bits

09e3f841

Nonce

4,785

Timestamp

10/9/2013, 6:53:13 AM

Confirmations

6,616,757

Mined by

⛏️ P2SHAN7xNeEXFpcryM41cuAkWQpeJWnwSpnoUT

Merkle Root

73d962533a72e8c41c4858387f091611585c6f52c8252b8074e1b55b28b82ae4

Transactions (4)

Coinbase06eba0ce92a314…b30fd90141b0b6

1 in → 1 out10.5900 XPM109 B

AN7xNeEX…nwSpnoUT

59a648f0bb0498…89b1676e2dcda4

239 in → 2 out273.0109 XPM34.62 KB

AZCE8Yae…GRvfu8kD AY9iVD2f…igVVQnBw

17680624af4697…7f7679b201e545

2 in → 2 out10.3900 XPM374 B

ASuoUi24…FwBoFbxd ARDJiHsZ…sFSYYmz5

f03915fb8cef83…916ce37800b30a

2 in → 2 out18.4269 XPM376 B

ANcvECzS…aCYUporj ALpthvGg…D1g5z4CT

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.

1.475 × 10⁹⁷(98-digit number)

14753098931314752700…10828377402413772799

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

1.475 × 10⁹⁷(98-digit number)

14753098931314752700…10828377402413772799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.475 × 10⁹⁷(98-digit number)

14753098931314752700…10828377402413772801

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

2.950 × 10⁹⁷(98-digit number)

29506197862629505400…21656754804827545599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.950 × 10⁹⁷(98-digit number)

29506197862629505400…21656754804827545601

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

5.901 × 10⁹⁷(98-digit number)

59012395725259010801…43313509609655091199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.901 × 10⁹⁷(98-digit number)

59012395725259010801…43313509609655091201

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

1.180 × 10⁹⁸(99-digit number)

11802479145051802160…86627019219310182399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.180 × 10⁹⁸(99-digit number)

11802479145051802160…86627019219310182401

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

2.360 × 10⁹⁸(99-digit number)

23604958290103604320…73254038438620364799

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 #200,864

Cookie Preferences