Block #809,298

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/13/2014, 12:06:30 PM · Difficulty 10.9734 · 6,008,158 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b26e065f7db8eb4b8a836563aa9b77a3f6fdeda55de4f416ad7e76990455b28

View on Chainz ↗

Height

#809,298

Difficulty

10.973435

Transactions

Size

6.45 KB

Version

Bits

0af9330b

Nonce

40,807,907

Timestamp

11/13/2014, 12:06:30 PM

Confirmations

6,008,158

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

28842a4709b11a3b267eaf583e40ce02ed139bb8c5907b44dd50f9d607da4a04

Transactions (3)

Coinbase053526dce46f41…821845dcd24edc

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

2f208cb33e7f73…9448bc9c97b781

43 in → 1 out238.9020 XPM5.60 KB

AJ83HaLh…EoKDggRk

f183dd9516c3fa…b82065ccd0ba3c

4 in → 2 out31.0180 XPM671 B

APTSdPLc…GLwfiPPf AQh73sjz…N6wFu4ue

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.

2.655 × 10⁹⁵(96-digit number)

26555587697078838605…63772425869884396719

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

2.655 × 10⁹⁵(96-digit number)

26555587697078838605…63772425869884396719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.655 × 10⁹⁵(96-digit number)

26555587697078838605…63772425869884396721

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

5.311 × 10⁹⁵(96-digit number)

53111175394157677210…27544851739768793439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.311 × 10⁹⁵(96-digit number)

53111175394157677210…27544851739768793441

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

1.062 × 10⁹⁶(97-digit number)

10622235078831535442…55089703479537586879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.062 × 10⁹⁶(97-digit number)

10622235078831535442…55089703479537586881

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

2.124 × 10⁹⁶(97-digit number)

21244470157663070884…10179406959075173759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.124 × 10⁹⁶(97-digit number)

21244470157663070884…10179406959075173761

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

4.248 × 10⁹⁶(97-digit number)

42488940315326141768…20358813918150347519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.248 × 10⁹⁶(97-digit number)

42488940315326141768…20358813918150347521

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

8.497 × 10⁹⁶(97-digit number)

84977880630652283536…40717627836300695039

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 #809,298

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