Block #2,645,028

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 6:08:02 PM · Difficulty 11.7227 · 4,188,306 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9acbcb77e5f59edb3ecdccfe741903914b876ab09963b7800b9316a003a7847

View on Chainz ↗

Height

#2,645,028

Difficulty

11.722659

Transactions

Size

1.01 KB

Version

Bits

0bb9002a

Nonce

213,878,626

Timestamp

5/2/2018, 6:08:02 PM

Confirmations

4,188,306

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e52c99601af3cb36a248f4f6280d0b7d6cd49ee6a1be12b0dd05ea086cbfaac4

Transactions (5)

Coinbasea1cfcd2ef723be…ab3637c5e11ddb

1 in → 1 out7.3000 XPM110 B

Adqah8zh…1WwoHJ9t

abd22d4888ae8c…0130f2b703b8c0

1 in → 2 out7.3700 XPM193 B

ATDfDwcd…yFkmQKrj AX9xvJyv…uiyTA55R

cf4ae0049ec467…95a80628fadd7c

1 in → 2 out7.3700 XPM192 B

AVcmujbJ…CJwjCkmp APvpRteY…19nMN894

d08000a45648d4…8387a90415dfcf

1 in → 2 out5.9954 XPM225 B

AQeX7WC7…2YPgjywP ALWZXB9F…VdyE4nsH

db756f64626caf…2e26d13b118562

1 in → 2 out2.7055 XPM227 B

AYUmL9uf…AN1fUu1e ALa9Z6aQ…Y9heUeLa

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.

3.635 × 10⁹⁴(95-digit number)

36350582433979685210…78021000831724181719

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

3.635 × 10⁹⁴(95-digit number)

36350582433979685210…78021000831724181719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.635 × 10⁹⁴(95-digit number)

36350582433979685210…78021000831724181721

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

7.270 × 10⁹⁴(95-digit number)

72701164867959370420…56042001663448363439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.270 × 10⁹⁴(95-digit number)

72701164867959370420…56042001663448363441

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

1.454 × 10⁹⁵(96-digit number)

14540232973591874084…12084003326896726879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.454 × 10⁹⁵(96-digit number)

14540232973591874084…12084003326896726881

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

2.908 × 10⁹⁵(96-digit number)

29080465947183748168…24168006653793453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.908 × 10⁹⁵(96-digit number)

29080465947183748168…24168006653793453761

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

5.816 × 10⁹⁵(96-digit number)

58160931894367496336…48336013307586907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.816 × 10⁹⁵(96-digit number)

58160931894367496336…48336013307586907521

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

1.163 × 10⁹⁶(97-digit number)

11632186378873499267…96672026615173815039

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 #2,645,028

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