Block #800,508

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/6/2014, 11:12:04 PM · Difficulty 10.9763 · 6,007,949 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

563ccc2191af34c2d51102b71408362aa51c6db72bd606a9bf535af0a9e1a535

View on Chainz ↗

Height

#800,508

Difficulty

10.976280

Transactions

Size

953 B

Version

Bits

0af9ed7a

Nonce

537,782,334

Timestamp

11/6/2014, 11:12:04 PM

Confirmations

6,007,949

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d681ff0817e2fced7886c86bfbeb053d8f7402975823af3b486c18b95bb3285e

Transactions (3)

Coinbase69992e9823454f…d52884f7074685

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

f6063aecfc83db…de4ff54cae78fb

3 in → 2 out1.2773 XPM520 B

Aa1tcDxw…KSwrKz5B Aba6XLEW…giia6sUh

88e0e4829261d8…bb6d4ce5c8b4e6

1 in → 2 out5.9401 XPM225 B

AGdWVjRk…LFVsqCnK AYoUM4Fs…LoF8KySX

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.

7.502 × 10⁹⁹(100-digit number)

75024818253152034535…90746932097062993919

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

7.502 × 10⁹⁹(100-digit number)

75024818253152034535…90746932097062993919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.502 × 10⁹⁹(100-digit number)

75024818253152034535…90746932097062993921

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

1.500 × 10¹⁰⁰(101-digit number)

15004963650630406907…81493864194125987839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.500 × 10¹⁰⁰(101-digit number)

15004963650630406907…81493864194125987841

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

3.000 × 10¹⁰⁰(101-digit number)

30009927301260813814…62987728388251975679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.000 × 10¹⁰⁰(101-digit number)

30009927301260813814…62987728388251975681

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

6.001 × 10¹⁰⁰(101-digit number)

60019854602521627628…25975456776503951359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.001 × 10¹⁰⁰(101-digit number)

60019854602521627628…25975456776503951361

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

1.200 × 10¹⁰¹(102-digit number)

12003970920504325525…51950913553007902719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.200 × 10¹⁰¹(102-digit number)

12003970920504325525…51950913553007902721

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

2.400 × 10¹⁰¹(102-digit number)

24007941841008651051…03901827106015805439

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 #800,508

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