Block #1,424,392

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/22/2016, 10:05:01 PM · Difficulty 10.7746 · 5,417,073 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

11af7c8fa34d01f5d2757d448710071c7af9ed6bbf621d0f6b0daea1924ab8b1

View on Chainz ↗

Height

#1,424,392

Difficulty

10.774559

Transactions

Size

904 B

Version

Bits

0ac64979

Nonce

7,618,405

Timestamp

1/22/2016, 10:05:01 PM

Confirmations

5,417,073

Mined by

⛏️ P2SHAVCMttrC9Afvd5oNWsGmJmHwBzvsfZM3RJ

Merkle Root

200e11629f1aa158cb614ddc8333d6b540f4e7169300ac1f8294b8c56210b8a2

Transactions (2)

Coinbase05ac46d6a93024…76b5476a141c07

1 in → 1 out8.6100 XPM110 B

AVCMttrC…vsfZM3RJ

2adff042b353f5…24ef2bc9ebad1f

1 in → 16 out270.5074 XPM703 B

ASpqLgqm…VZMfCZZm AHQqNjLy…615wEyKQ AMRvoQuL…5Dw7CEhj Ac3qDtW5…8bYZSGfW AcTyYdTB…Au15J5gk

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.

8.880 × 10⁹⁵(96-digit number)

88804084805935807613…17746594511321991679

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

8.880 × 10⁹⁵(96-digit number)

88804084805935807613…17746594511321991679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.880 × 10⁹⁵(96-digit number)

88804084805935807613…17746594511321991681

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

1.776 × 10⁹⁶(97-digit number)

17760816961187161522…35493189022643983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.776 × 10⁹⁶(97-digit number)

17760816961187161522…35493189022643983361

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

3.552 × 10⁹⁶(97-digit number)

35521633922374323045…70986378045287966719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.552 × 10⁹⁶(97-digit number)

35521633922374323045…70986378045287966721

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

7.104 × 10⁹⁶(97-digit number)

71043267844748646090…41972756090575933439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.104 × 10⁹⁶(97-digit number)

71043267844748646090…41972756090575933441

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

1.420 × 10⁹⁷(98-digit number)

14208653568949729218…83945512181151866879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.420 × 10⁹⁷(98-digit number)

14208653568949729218…83945512181151866881

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

2.841 × 10⁹⁷(98-digit number)

28417307137899458436…67891024362303733759

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 #1,424,392

Cookie Preferences