Block #800,392

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/6/2014, 9:21:37 PM · Difficulty 10.9762 · 5,995,584 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b729cfc69120cd40383ca44e951de836b79f6b0ed09d8ca33923a6589fb77f99

View on Chainz ↗

Height

#800,392

Difficulty

10.976247

Transactions

Size

1.15 KB

Version

Bits

0af9eb57

Nonce

1,351,353,971

Timestamp

11/6/2014, 9:21:37 PM

Confirmations

5,995,584

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9f6ceecb4e205c46689e021325cefcdee060cfa95d8d5a6f2e12e5b0d227446d

Transactions (2)

Coinbase01d6d6ce1e137a…c7a459f395baec

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

84afd4e9257eda…bf5635743fb117

6 in → 2 out9.7257 XPM967 B

AMvDEhZv…V5YvJTWj AZQxzEMH…QTN7ziMd

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.

2.136 × 10⁹⁷(98-digit number)

21363319040003012340…70561727786119403519

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

2.136 × 10⁹⁷(98-digit number)

21363319040003012340…70561727786119403519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.136 × 10⁹⁷(98-digit number)

21363319040003012340…70561727786119403521

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

4.272 × 10⁹⁷(98-digit number)

42726638080006024681…41123455572238807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.272 × 10⁹⁷(98-digit number)

42726638080006024681…41123455572238807041

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

8.545 × 10⁹⁷(98-digit number)

85453276160012049362…82246911144477614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.545 × 10⁹⁷(98-digit number)

85453276160012049362…82246911144477614081

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

1.709 × 10⁹⁸(99-digit number)

17090655232002409872…64493822288955228159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.709 × 10⁹⁸(99-digit number)

17090655232002409872…64493822288955228161

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

3.418 × 10⁹⁸(99-digit number)

34181310464004819744…28987644577910456319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.418 × 10⁹⁸(99-digit number)

34181310464004819744…28987644577910456321

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