Block #1,568,996

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2016, 4:07:43 PM · Difficulty 10.7570 · 5,249,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

372b4ec4fd5c2bab321c738fec37fbfb5b019af4d5f7c886328b7b9b49777343

View on Chainz ↗

Height

#1,568,996

Difficulty

10.757036

Transactions

Size

1.21 KB

Version

Bits

0ac1cd24

Nonce

513,012,307

Timestamp

5/2/2016, 4:07:43 PM

Confirmations

5,249,012

Mined by

⛏️ P2SHAJD3viM7Lz1Ydru9Vibwi6VumVa4XdLusf

Merkle Root

ccf12fd8cc0860d55e34d9a5b35b207dc260db86e71ba7c735f3f8695635674b

Transactions (2)

Coinbaseca771427943b2b…54171f482894d2

1 in → 1 out8.6500 XPM110 B

AJD3viM7…a4XdLusf

94f8c566da9051…4ad20c307511d6

1 in → 26 out165.9914 XPM1.02 KB

AJRD5vZ8…fTRx2Niz AXGcM2i5…UnbSvZvd AXz5TNiY…3MzCDaDH AQDRamJM…WDFTQomU Ae28a42r…k7KMYFgV

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.

1.014 × 10⁹⁶(97-digit number)

10142188207995355858…42216925704039423999

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

1.014 × 10⁹⁶(97-digit number)

10142188207995355858…42216925704039423999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.014 × 10⁹⁶(97-digit number)

10142188207995355858…42216925704039424001

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

2.028 × 10⁹⁶(97-digit number)

20284376415990711717…84433851408078847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.028 × 10⁹⁶(97-digit number)

20284376415990711717…84433851408078848001

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

4.056 × 10⁹⁶(97-digit number)

40568752831981423435…68867702816157695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.056 × 10⁹⁶(97-digit number)

40568752831981423435…68867702816157696001

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

8.113 × 10⁹⁶(97-digit number)

81137505663962846871…37735405632315391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.113 × 10⁹⁶(97-digit number)

81137505663962846871…37735405632315392001

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

1.622 × 10⁹⁷(98-digit number)

16227501132792569374…75470811264630783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.622 × 10⁹⁷(98-digit number)

16227501132792569374…75470811264630784001

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 #1,568,996

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