Block #2,825,838

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/5/2018, 12:56:42 PM · Difficulty 11.7101 · 4,010,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23f672e7e37f9a98f360e5d1b2d47d1824114e1945f938c408134d48f1869276

View on Chainz ↗

Height

#2,825,838

Difficulty

11.710093

Transactions

Size

1.34 KB

Version

Bits

0bb5c8a2

Nonce

257,548,343

Timestamp

9/5/2018, 12:56:42 PM

Confirmations

4,010,756

Mined by

⛏️ P2SHAcLLSNgQTXbR6XeKw6D6g8tHS1QrfjP5Kd

Merkle Root

3b695743b8d927421d552e42562de0472e8465cb389ab828ffa2dffee2e72f5b

Transactions (4)

Coinbasea2b9653adb99b4…cba5250fda2d9c

1 in → 1 out7.3200 XPM110 B

AcLLSNgQ…QrfjP5Kd

19b163b9dbc344…31de4181763a3a

1 in → 2 out7.2800 XPM193 B

AbRCocDs…d4UfUwey AQqvFqxG…LT9rHjCu

ac38466a6b058c…29e982d6784480

5 in → 2 out20.0310 XPM750 B

AbYnx9NL…rJTNKxsW AQFKhTML…asVdWKXV

dc7a9e404058d1…dc01b3ac3c2de6

1 in → 2 out1.1832 XPM227 B

ANjTQp24…sVkz8Xup AQLo2Uh6…GGfQiZBs

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.

6.338 × 10⁹⁴(95-digit number)

63384076021319751936…21432946096088010239

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

6.338 × 10⁹⁴(95-digit number)

63384076021319751936…21432946096088010239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.338 × 10⁹⁴(95-digit number)

63384076021319751936…21432946096088010241

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

1.267 × 10⁹⁵(96-digit number)

12676815204263950387…42865892192176020479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.267 × 10⁹⁵(96-digit number)

12676815204263950387…42865892192176020481

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

2.535 × 10⁹⁵(96-digit number)

25353630408527900774…85731784384352040959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.535 × 10⁹⁵(96-digit number)

25353630408527900774…85731784384352040961

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

5.070 × 10⁹⁵(96-digit number)

50707260817055801548…71463568768704081919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.070 × 10⁹⁵(96-digit number)

50707260817055801548…71463568768704081921

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

1.014 × 10⁹⁶(97-digit number)

10141452163411160309…42927137537408163839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.014 × 10⁹⁶(97-digit number)

10141452163411160309…42927137537408163841

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.028 × 10⁹⁶(97-digit number)

20282904326822320619…85854275074816327679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,825,838

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