Block #3,403,646

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/23/2019, 3:02:34 PM · Difficulty 10.9868 · 3,422,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7f83d019cf9a165456120047bee35c001ddadae9ee06ce177c16495c8720664

View on Chainz ↗

Height

#3,403,646

Difficulty

10.986823

Transactions

Size

2.15 KB

Version

Bits

0afca074

Nonce

1,126,353,971

Timestamp

10/23/2019, 3:02:34 PM

Confirmations

3,422,602

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

a838355d0375a94137422092e523cc108bf4c9fb0452b792be6d81590683c246

Transactions (4)

Coinbase0c6455510cb001…75a93ee8a66367

1 in → 1 out8.3100 XPM110 B

ASiq2qtK…VMhmk7yL

bd1b0f01792169…3a5a61c33aa944

9 in → 2 out50.0327 XPM1.18 KB

AbNUu9xr…SFUXCj5W ASiq2qtK…VMhmk7yL

dc07c61947ca4b…c9945c694d1736

3 in → 2 out23.0453 XPM454 B

ASiq2qtK…VMhmk7yL AdGFnV3a…o6n2zX3x

023c4ff103c4a8…81ad907b538c4c

2 in → 2 out14.7900 XPM341 B

ActuaCsV…dD3zry5m AeHXpz5Q…WLPHByEV

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.

9.655 × 10⁹³(94-digit number)

96550240146473996643…18044022234130186239

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

9.655 × 10⁹³(94-digit number)

96550240146473996643…18044022234130186239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.655 × 10⁹³(94-digit number)

96550240146473996643…18044022234130186241

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

1.931 × 10⁹⁴(95-digit number)

19310048029294799328…36088044468260372479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.931 × 10⁹⁴(95-digit number)

19310048029294799328…36088044468260372481

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

3.862 × 10⁹⁴(95-digit number)

38620096058589598657…72176088936520744959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.862 × 10⁹⁴(95-digit number)

38620096058589598657…72176088936520744961

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

7.724 × 10⁹⁴(95-digit number)

77240192117179197314…44352177873041489919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.724 × 10⁹⁴(95-digit number)

77240192117179197314…44352177873041489921

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

1.544 × 10⁹⁵(96-digit number)

15448038423435839462…88704355746082979839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.544 × 10⁹⁵(96-digit number)

15448038423435839462…88704355746082979841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #3,403,646

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