Block #851,987

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/13/2014, 5:39:45 PM · Difficulty 10.9702 · 5,958,996 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3373c94102fd53a0812ee113f5b1c8c8281d5a196c43e3ac6dd63e7353d0d80

View on Chainz ↗

Height

#851,987

Difficulty

10.970249

Transactions

Size

1.66 KB

Version

Bits

0af8623c

Nonce

1,076,608,826

Timestamp

12/13/2014, 5:39:45 PM

Confirmations

5,958,996

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

363b6968a54122fefd16d2aafba3753ec125bc99a2b1c81f67bd146ce7e9aab9

Transactions (5)

Coinbase88b457c560b27f…4cbff0acde3c85

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

3c29f1d68c8cc4…56e6c5eb3c5d08

3 in → 2 out23.0775 XPM523 B

AeveCGBm…8o3QdP1Y AQdb61ey…Etuce5Lv

b8ed50ff67e3dd…832f5dbf36c5da

1 in → 2 out7.2136 XPM226 B

ATjwywoV…ga9eRXwi AeFRuUAh…hGTKzQWd

5c685ba7342aa5…340c46a95e0a3c

1 in → 2 out7.2129 XPM226 B

AU3EgHPb…DCRaDoTM AYEdi4iJ…Dm8VoQdS

507dc77eeb357e…66d69ac2377584

3 in → 2 out1.5149 XPM523 B

AbRkNGDK…JGFvXTr5 AHRoBSh4…BSVTQ36Q

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.

6.942 × 10⁹⁵(96-digit number)

69428698989863081519…88945649953281396439

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

6.942 × 10⁹⁵(96-digit number)

69428698989863081519…88945649953281396439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.942 × 10⁹⁵(96-digit number)

69428698989863081519…88945649953281396441

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

1.388 × 10⁹⁶(97-digit number)

13885739797972616303…77891299906562792879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.388 × 10⁹⁶(97-digit number)

13885739797972616303…77891299906562792881

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

2.777 × 10⁹⁶(97-digit number)

27771479595945232607…55782599813125585759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.777 × 10⁹⁶(97-digit number)

27771479595945232607…55782599813125585761

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

5.554 × 10⁹⁶(97-digit number)

55542959191890465215…11565199626251171519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.554 × 10⁹⁶(97-digit number)

55542959191890465215…11565199626251171521

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

1.110 × 10⁹⁷(98-digit number)

11108591838378093043…23130399252502343039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.110 × 10⁹⁷(98-digit number)

11108591838378093043…23130399252502343041

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

2.221 × 10⁹⁷(98-digit number)

22217183676756186086…46260798505004686079

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 #851,987

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