Block #2,815,432

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/29/2018, 2:49:07 PM · Difficulty 11.6834 · 4,022,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

397cec240c05915769daa65738fb783f2b324584452faef4adefa111e47729fd

View on Chainz ↗

Height

#2,815,432

Difficulty

11.683427

Transactions

Size

2.17 KB

Version

Bits

0baef513

Nonce

760,369,430

Timestamp

8/29/2018, 2:49:07 PM

Confirmations

4,022,977

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

a842ea9bf1bb27450587800be877563bde543e6490bf52a047f23244b7e22c99

Transactions (3)

Coinbase9b0b4d25ed4640…b1e37731afefbe

1 in → 1 out7.3400 XPM110 B

AZtxQr2F…7grUWrUz

cbbbf6867cb1c1…d854b7c7c5ee82

12 in → 2 out50.0497 XPM1.61 KB

AP7BXaXU…dhftneEJ AVeV4S3e…YngoJzRw

3f9eae8a6e093d…5b87019e5650f3

2 in → 2 out4.5877 XPM375 B

Af6Bp78e…sg3hjgNh ANxNfXmZ…4p5PaHCM

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.

4.541 × 10⁹⁶(97-digit number)

45418696379290014356…52298776801830010879

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

4.541 × 10⁹⁶(97-digit number)

45418696379290014356…52298776801830010879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.541 × 10⁹⁶(97-digit number)

45418696379290014356…52298776801830010881

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

9.083 × 10⁹⁶(97-digit number)

90837392758580028713…04597553603660021759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.083 × 10⁹⁶(97-digit number)

90837392758580028713…04597553603660021761

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

1.816 × 10⁹⁷(98-digit number)

18167478551716005742…09195107207320043519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.816 × 10⁹⁷(98-digit number)

18167478551716005742…09195107207320043521

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

3.633 × 10⁹⁷(98-digit number)

36334957103432011485…18390214414640087039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.633 × 10⁹⁷(98-digit number)

36334957103432011485…18390214414640087041

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

7.266 × 10⁹⁷(98-digit number)

72669914206864022970…36780428829280174079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.266 × 10⁹⁷(98-digit number)

72669914206864022970…36780428829280174081

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

1.453 × 10⁹⁸(99-digit number)

14533982841372804594…73560857658560348159

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.453 × 10⁹⁸(99-digit number)

14533982841372804594…73560857658560348161

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 #2,815,432

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