Block #3,640,203

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2020, 9:12:39 AM · Difficulty 10.9080 · 3,201,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1694442d3c89096593ab0566f1c2a822f07e9601b9c03adb25f003d60cdce022

View on Chainz ↗

Height

#3,640,203

Difficulty

10.907955

Transactions

Size

8.17 KB

Version

Bits

0ae86fc5

Nonce

750,073,732

Timestamp

4/12/2020, 9:12:39 AM

Confirmations

3,201,284

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

c3332ef965d5dc062030e4cfee798673d381a96946584a019a61d3bb4b42d327

Transactions (3)

Coinbaseb533c98ba7198e…d8f542c8d598f2

1 in → 1 out8.4800 XPM109 B

ASiq2qtK…VMhmk7yL

e6af252fbdd9a2…1b0e850de36c5f

60 in → 2 out501.6374 XPM6.80 KB

ASiq2qtK…VMhmk7yL Ab5fFXVt…EC9k8a2d

66a577995f864a…00f6f13fb9e975

9 in → 2 out50.5062 XPM1.17 KB

AdGFnV3a…o6n2zX3x ASiq2qtK…VMhmk7yL

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.

1.237 × 10⁹⁶(97-digit number)

12375090088817286382…10616455052618598399

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

1.237 × 10⁹⁶(97-digit number)

12375090088817286382…10616455052618598399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.237 × 10⁹⁶(97-digit number)

12375090088817286382…10616455052618598401

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

2.475 × 10⁹⁶(97-digit number)

24750180177634572764…21232910105237196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.475 × 10⁹⁶(97-digit number)

24750180177634572764…21232910105237196801

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

4.950 × 10⁹⁶(97-digit number)

49500360355269145528…42465820210474393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.950 × 10⁹⁶(97-digit number)

49500360355269145528…42465820210474393601

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

9.900 × 10⁹⁶(97-digit number)

99000720710538291056…84931640420948787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.900 × 10⁹⁶(97-digit number)

99000720710538291056…84931640420948787201

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

1.980 × 10⁹⁷(98-digit number)

19800144142107658211…69863280841897574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.980 × 10⁹⁷(98-digit number)

19800144142107658211…69863280841897574401

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 #3,640,203

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