Block #320,408

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 3:29:56 PM · Difficulty 10.1823 · 6,493,901 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce0ce3360a1bf2d82cae5f77bde72748b0594fba204c1b088d4b5841887f12de

View on Chainz ↗

Height

#320,408

Difficulty

10.182321

Transactions

Size

16.39 KB

Version

Bits

0a2eac97

Nonce

6,884

Timestamp

12/19/2013, 3:29:56 PM

Confirmations

6,493,901

Mined by

⛏️ P2SHAVZgkCcWPrF4B5ENWiQHiKUwrnyETyJHFA

Merkle Root

82ecdfbdd9b8e27b12d503646cd8cd9b177073166f6a2050de8a88fa7bbbeed1

Transactions (3)

Coinbaseea4ece91bc3e30…3091ccd0b40e7e

1 in → 1 out9.8100 XPM109 B

AVZgkCcW…yETyJHFA

275b0bc31de458…d8051fdfa6b9fd

110 in → 2 out36.2307 XPM15.97 KB

AaBxrhEb…1EgrpnCR Adh1di8t…Xgh24Jr6

a444adcfabc162…06c61bd5fc4323

1 in → 2 out3.2395 XPM226 B

AbDfY7nx…WiAEBof9 AeMG3MbB…Yn1ndGmN

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.

2.059 × 10⁹⁶(97-digit number)

20599428568311687899…05792908145799303679

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

2.059 × 10⁹⁶(97-digit number)

20599428568311687899…05792908145799303679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.059 × 10⁹⁶(97-digit number)

20599428568311687899…05792908145799303681

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

4.119 × 10⁹⁶(97-digit number)

41198857136623375799…11585816291598607359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.119 × 10⁹⁶(97-digit number)

41198857136623375799…11585816291598607361

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

8.239 × 10⁹⁶(97-digit number)

82397714273246751599…23171632583197214719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.239 × 10⁹⁶(97-digit number)

82397714273246751599…23171632583197214721

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

1.647 × 10⁹⁷(98-digit number)

16479542854649350319…46343265166394429439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.647 × 10⁹⁷(98-digit number)

16479542854649350319…46343265166394429441

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

3.295 × 10⁹⁷(98-digit number)

32959085709298700639…92686530332788858879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.295 × 10⁹⁷(98-digit number)

32959085709298700639…92686530332788858881

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 #320,408

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