Block #2,646,143

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 5:35:20 AM · Difficulty 11.7452 · 4,184,380 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e9e0c0d52211e414596781f33a807fb9a4838cf7a2b334c12b8fc80a13837dc

View on Chainz ↗

Height

#2,646,143

Difficulty

11.745213

Transactions

Size

1.72 KB

Version

Bits

0bbec640

Nonce

297,030,260

Timestamp

5/3/2018, 5:35:20 AM

Confirmations

4,184,380

Mined by

⛏️ P2SHALWUM56Dux9Kvsg95saVEA5Y1TTJ4btZih

Merkle Root

6e6ebb5860b5b2fa064acecd4835557ca254a4c89e6d320c559bd9fff351500f

Transactions (4)

Coinbasee3529e2eb5af14…13616d4f3bf499

1 in → 1 out7.2700 XPM110 B

ALWUM56D…TJ4btZih

5e98e34d96db39…03fde26dd3dc54

1 in → 2 out6.4437 XPM226 B

ARznVePF…S7wvbB9s ASpWAdSV…CRNTEpVH

0170a31a3195e0…11d7bf299ca3a8

4 in → 2 out84.1018 XPM670 B

AP4UTDoB…3rxU9GyP AcPsbh66…WyGDfnCd

7cfc3cdea79fc2…5356e393080cea

4 in → 2 out0.0475 XPM668 B

APi8C85f…Lg5MDiei AVQ3muZJ…MDmXoVWL

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.

2.514 × 10⁹⁸(99-digit number)

25140855783646139113…75959848011723243519

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

2.514 × 10⁹⁸(99-digit number)

25140855783646139113…75959848011723243519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.514 × 10⁹⁸(99-digit number)

25140855783646139113…75959848011723243521

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

5.028 × 10⁹⁸(99-digit number)

50281711567292278226…51919696023446487039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.028 × 10⁹⁸(99-digit number)

50281711567292278226…51919696023446487041

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

1.005 × 10⁹⁹(100-digit number)

10056342313458455645…03839392046892974079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.005 × 10⁹⁹(100-digit number)

10056342313458455645…03839392046892974081

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

2.011 × 10⁹⁹(100-digit number)

20112684626916911290…07678784093785948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.011 × 10⁹⁹(100-digit number)

20112684626916911290…07678784093785948161

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

4.022 × 10⁹⁹(100-digit number)

40225369253833822581…15357568187571896319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.022 × 10⁹⁹(100-digit number)

40225369253833822581…15357568187571896321

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

8.045 × 10⁹⁹(100-digit number)

80450738507667645162…30715136375143792639

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 #2,646,143

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