Block #855,292

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2014, 6:03:51 AM · Difficulty 10.9684 · 5,984,583 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f60e0f8b71447c6a8807336832ad7b0a08492123b26fce3ffc928201f5f5b5b

View on Chainz ↗

Height

#855,292

Difficulty

10.968400

Transactions

Size

8.59 KB

Version

Bits

0af7e908

Nonce

532,198,003

Timestamp

12/16/2014, 6:03:51 AM

Confirmations

5,984,583

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

107b246217516503fcc35828ad5b433d93654f00783f81278a94e87e8f93f342

Transactions (3)

Coinbase5a071756230c44…9aeda7dbbc618e

1 in → 1 out8.4050 XPM116 B

ANSXnLY2…Sd25TjkD

166e105f15afd3…71f3e27a938811

56 in → 2 out500.0100 XPM8.17 KB

AP5VwWQd…6tAkTyKG AJjnK9uC…VreFquR4

3a0e903a9b92b2…962d739d374df3

1 in → 2 out0.0641 XPM226 B

AW7oX2TP…F6TfxH5Z AWZA24Kj…MyXWhUpj

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.

1.660 × 10¹⁰¹(102-digit number)

16605626369658505791…08094857522084904959

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

1.660 × 10¹⁰¹(102-digit number)

16605626369658505791…08094857522084904959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.660 × 10¹⁰¹(102-digit number)

16605626369658505791…08094857522084904961

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

3.321 × 10¹⁰¹(102-digit number)

33211252739317011582…16189715044169809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.321 × 10¹⁰¹(102-digit number)

33211252739317011582…16189715044169809921

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

6.642 × 10¹⁰¹(102-digit number)

66422505478634023164…32379430088339619839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.642 × 10¹⁰¹(102-digit number)

66422505478634023164…32379430088339619841

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

1.328 × 10¹⁰²(103-digit number)

13284501095726804632…64758860176679239679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.328 × 10¹⁰²(103-digit number)

13284501095726804632…64758860176679239681

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

2.656 × 10¹⁰²(103-digit number)

26569002191453609265…29517720353358479359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.656 × 10¹⁰²(103-digit number)

26569002191453609265…29517720353358479361

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 #855,292

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