Block #3,244,038

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/28/2019, 2:16:06 AM · Difficulty 11.0062 · 3,598,038 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

faa8ebe0053b373b2f71764f198d82e321772ba133228acd323e2085093db780

View on Chainz ↗

Height

#3,244,038

Difficulty

11.006244

Transactions

Size

1.41 KB

Version

Bits

0b019937

Nonce

386,649,521

Timestamp

6/28/2019, 2:16:06 AM

Confirmations

3,598,038

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

f09efefed2d3f45dd8783ab43ccd0885fc8e0eb99a41e6a781c2db5c10924323

Transactions (5)

Coinbase017be78f663e74…bef7facc0c8dbf

1 in → 1 out8.2800 XPM110 B

ASiq2qtK…VMhmk7yL

d4891eb857fabb…050f91b67ae896

2 in → 2 out16.4700 XPM306 B

ASiq2qtK…VMhmk7yL AdGFnV3a…o6n2zX3x

6154362c049e69…c3fed531950c4d

2 in → 2 out11.4587 XPM339 B

ASiq2qtK…VMhmk7yL AdUnfZPJ…CfnSTpQz

5eb015e568630a…5b6ee90bed2bb5

1 in → 2 out4.3480 XPM226 B

AJtQNmM4…XBRjaQ6m ASiq2qtK…VMhmk7yL

cef8c59d737f6d…f1656e92f90e27

2 in → 2 out4.5772 XPM373 B

ANC1Y3CU…VSjzaudy 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.

3.671 × 10⁹²(93-digit number)

36712080133341505189…29307400391401726459

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

3.671 × 10⁹²(93-digit number)

36712080133341505189…29307400391401726459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.671 × 10⁹²(93-digit number)

36712080133341505189…29307400391401726461

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

7.342 × 10⁹²(93-digit number)

73424160266683010378…58614800782803452919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.342 × 10⁹²(93-digit number)

73424160266683010378…58614800782803452921

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

1.468 × 10⁹³(94-digit number)

14684832053336602075…17229601565606905839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.468 × 10⁹³(94-digit number)

14684832053336602075…17229601565606905841

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

2.936 × 10⁹³(94-digit number)

29369664106673204151…34459203131213811679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.936 × 10⁹³(94-digit number)

29369664106673204151…34459203131213811681

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

5.873 × 10⁹³(94-digit number)

58739328213346408303…68918406262427623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.873 × 10⁹³(94-digit number)

58739328213346408303…68918406262427623361

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.174 × 10⁹⁴(95-digit number)

11747865642669281660…37836812524855246719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #3,244,038

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