Block #858,195

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2014, 10:36:35 AM · Difficulty 10.9669 · 5,975,375 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1211ecc770b897054dca27f86d26eda19855c7794f3985158be27e7bd70365b7

View on Chainz ↗

Height

#858,195

Difficulty

10.966883

Transactions

Size

886 B

Version

Bits

0af785a9

Nonce

1,914,360,801

Timestamp

12/18/2014, 10:36:35 AM

Confirmations

5,975,375

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ebb7510854e8591ea49044cc1eb6424f5374ea7fa86d49d7ae5617f909346b82

Transactions (4)

Coinbase4c31982ac49903…c2e1f730d49b00

1 in → 1 out8.3450 XPM116 B

ANSXnLY2…Sd25TjkD

dec9658f4ba2d0…ab3d3d1e6f2a13

1 in → 2 out0.1182 XPM226 B

AWW85trw…NMeDbtpD ASsP4YUs…vW7D39i9

d83581bfbae50e…8c7b5c22b6fac6

1 in → 2 out0.0231 XPM226 B

Ae5CvRpW…NAvXRe4E AaTQxcyn…YXhZKnBJ

0fc252323ac12a…c07800616653b4

1 in → 2 out0.0998 XPM227 B

AM9c8EkA…QqKDDZig AM74aTrp…HSABmNd5

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.

4.896 × 10⁹⁶(97-digit number)

48960381401546349061…91318275681500999679

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

4.896 × 10⁹⁶(97-digit number)

48960381401546349061…91318275681500999679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.896 × 10⁹⁶(97-digit number)

48960381401546349061…91318275681500999681

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

9.792 × 10⁹⁶(97-digit number)

97920762803092698123…82636551363001999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.792 × 10⁹⁶(97-digit number)

97920762803092698123…82636551363001999361

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

1.958 × 10⁹⁷(98-digit number)

19584152560618539624…65273102726003998719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.958 × 10⁹⁷(98-digit number)

19584152560618539624…65273102726003998721

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

3.916 × 10⁹⁷(98-digit number)

39168305121237079249…30546205452007997439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.916 × 10⁹⁷(98-digit number)

39168305121237079249…30546205452007997441

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

7.833 × 10⁹⁷(98-digit number)

78336610242474158498…61092410904015994879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.833 × 10⁹⁷(98-digit number)

78336610242474158498…61092410904015994881

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 #858,195

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