Block #320,233

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 12:45:52 PM · Difficulty 10.1804 · 6,489,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e28665d70323c061456af82a526e6a885d434efa8c240565af7f4278da960b4

View on Chainz ↗

Height

#320,233

Difficulty

10.180440

Transactions

Size

1.05 KB

Version

Bits

0a2e3152

Nonce

43,374

Timestamp

12/19/2013, 12:45:52 PM

Confirmations

6,489,302

Mined by

⛏️ aRtAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

9c58d17fbeb31713f845ae56ae6cd2b94fb856debbb1fb154625769d2650ca7e

Transactions (1)

Coinbase9c58d17fbeb317…25769d2650ca7e

1 in → 27 out9.6300 XPM981 B

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AZemWJAo…6jhDtieG ASWX42VM…XypQABkY AUQ45PZs…3pQWh7gW

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.

1.889 × 10⁹⁴(95-digit number)

18897897153302511525…98077133011866841279

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

1.889 × 10⁹⁴(95-digit number)

18897897153302511525…98077133011866841279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.889 × 10⁹⁴(95-digit number)

18897897153302511525…98077133011866841281

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

3.779 × 10⁹⁴(95-digit number)

37795794306605023050…96154266023733682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.779 × 10⁹⁴(95-digit number)

37795794306605023050…96154266023733682561

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

7.559 × 10⁹⁴(95-digit number)

75591588613210046101…92308532047467365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.559 × 10⁹⁴(95-digit number)

75591588613210046101…92308532047467365121

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

1.511 × 10⁹⁵(96-digit number)

15118317722642009220…84617064094934730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.511 × 10⁹⁵(96-digit number)

15118317722642009220…84617064094934730241

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

3.023 × 10⁹⁵(96-digit number)

30236635445284018440…69234128189869460479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.023 × 10⁹⁵(96-digit number)

30236635445284018440…69234128189869460481

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 #320,233

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