Block #373,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 5:43:34 AM · Difficulty 10.4253 · 6,443,526 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41e5b53610ecced93048fbf64afa0b1acfaaa98e5b69cc0077b26064a6891a41

View on Chainz ↗

Height

#373,320

Difficulty

10.425279

Transactions

Size

1.20 KB

Version

Bits

0a6cdf14

Nonce

79,693

Timestamp

1/24/2014, 5:43:34 AM

Confirmations

6,443,526

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6bcd9d5693316aadb98fe9056872c9fee3177cf6ea5c342e2bfefad4c4a6cdf0

Transactions (5)

Coinbase516e7bc4da92b6…7e530639214796

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

97f1f48b6c3416…e04880776f3b72

2 in → 1 out124.6500 XPM341 B

AQUC7Hue…LL2XMoNY

cf32e18d2301f4…739652dfe1b29d

1 in → 2 out4.0655 XPM226 B

AUztPXSy…PYnBnvu6 Aec7DQEq…xxHG9vW4

094025e2917c1d…c46bb60e4a12d6

1 in → 2 out1.2777 XPM225 B

AXNVLKpH…GHdwoAxs AM1vawpG…g4yyXaHo

66439ac18c45d1…5e2d2939187891

1 in → 2 out4.0316 XPM227 B

AS39ceDG…WGqk261H ANFSkqVE…zZgkQHwv

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.

5.547 × 10⁹⁵(96-digit number)

55473364229430564800…00589099544904918899

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

5.547 × 10⁹⁵(96-digit number)

55473364229430564800…00589099544904918899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.547 × 10⁹⁵(96-digit number)

55473364229430564800…00589099544904918901

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

1.109 × 10⁹⁶(97-digit number)

11094672845886112960…01178199089809837799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.109 × 10⁹⁶(97-digit number)

11094672845886112960…01178199089809837801

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

2.218 × 10⁹⁶(97-digit number)

22189345691772225920…02356398179619675599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.218 × 10⁹⁶(97-digit number)

22189345691772225920…02356398179619675601

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

4.437 × 10⁹⁶(97-digit number)

44378691383544451840…04712796359239351199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.437 × 10⁹⁶(97-digit number)

44378691383544451840…04712796359239351201

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

8.875 × 10⁹⁶(97-digit number)

88757382767088903680…09425592718478702399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.875 × 10⁹⁶(97-digit number)

88757382767088903680…09425592718478702401

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 #373,320

Cookie Preferences