Block #2,643,255

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/2/2018, 1:07:05 AM · Difficulty 11.6780 · 4,187,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a8c4ceeb61e8c1c63cb9ccf4ec0de8b457b5cd65ed32a776643ccd79a0be4e5

View on Chainz ↗

Height

#2,643,255

Difficulty

11.677971

Transactions

Size

1.08 KB

Version

Bits

0bad8f82

Nonce

61,397,892

Timestamp

5/2/2018, 1:07:05 AM

Confirmations

4,187,374

Mined by

⛏️ P2SHAPqDfn1B2Au7Axvgoq3VZri29zJjX9iko9

Merkle Root

9d2fe9a6518cf16dccdfd2f479d4d58ac094552d78f4422d68be4039e82710fa

Transactions (5)

Coinbasef374da5be8320c…7ffbe935dcbc12

1 in → 1 out7.3600 XPM110 B

APqDfn1B…JjX9iko9

ae025ae2a73fcf…6d3fe0a8f57c0a

1 in → 2 out6.9210 XPM227 B

AS8kn3mG…FQqPNRKc AYrVVyHX…izr1k7kM

2d829a4f02f871…e52f74cea1a102

1 in → 2 out6.3029 XPM225 B

AXU2VgsN…RePZXTgf AcmhrY9s…hrMMr1dT

bdb3f5b42083a9…74359cb446d5c1

1 in → 2 out6.2406 XPM226 B

AJN1ao9K…CUKW4qu3 ANCjbJ3j…jEULQYWx

55f12635a17b9a…8865dccef631be

1 in → 2 out2.4229 XPM227 B

AGa3obRH…X1wpixsr Ac9uvTro…oEm1KfU8

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.

3.144 × 10⁹⁷(98-digit number)

31441296519650531571…58083639197643448319

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

3.144 × 10⁹⁷(98-digit number)

31441296519650531571…58083639197643448319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.144 × 10⁹⁷(98-digit number)

31441296519650531571…58083639197643448321

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

6.288 × 10⁹⁷(98-digit number)

62882593039301063142…16167278395286896639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.288 × 10⁹⁷(98-digit number)

62882593039301063142…16167278395286896641

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

1.257 × 10⁹⁸(99-digit number)

12576518607860212628…32334556790573793279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.257 × 10⁹⁸(99-digit number)

12576518607860212628…32334556790573793281

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

2.515 × 10⁹⁸(99-digit number)

25153037215720425257…64669113581147586559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.515 × 10⁹⁸(99-digit number)

25153037215720425257…64669113581147586561

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

5.030 × 10⁹⁸(99-digit number)

50306074431440850514…29338227162295173119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.030 × 10⁹⁸(99-digit number)

50306074431440850514…29338227162295173121

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

1.006 × 10⁹⁹(100-digit number)

10061214886288170102…58676454324590346239

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.006 × 10⁹⁹(100-digit number)

10061214886288170102…58676454324590346241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,643,255

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