Block #535,192

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/10/2014, 6:53:32 PM · Difficulty 10.9039 · 6,291,565 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b08e1d5e918626cca7185f9006968adfaaaaf23e9d823716f9746f77c4880631

View on Chainz ↗

Height

#535,192

Difficulty

10.903915

Transactions

Size

957 B

Version

Bits

0ae766f2

Nonce

48,158

Timestamp

5/10/2014, 6:53:32 PM

Confirmations

6,291,565

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

4586e88ded188ba81f0661d9c563a5c562c071b08a5933edd342b1960518d68d

Transactions (2)

Coinbasec723b60e7e55b6…8db2f01d1ff862

1 in → 17 out8.4100 XPM641 B

AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AbPcCMg4…719q6mAX ATp4jJhs…TbSgR8Qb AZdy7tMB…bWoKDJVg

9d9ced1dd6fc46…885efcefa24a59

1 in → 2 out2.3457 XPM226 B

AeKRGLL4…saTinZec AToctXWm…mgEtBv9N

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.

8.478 × 10⁹⁴(95-digit number)

84782815345530940095…97444509045065689599

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

8.478 × 10⁹⁴(95-digit number)

84782815345530940095…97444509045065689599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.478 × 10⁹⁴(95-digit number)

84782815345530940095…97444509045065689601

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

1.695 × 10⁹⁵(96-digit number)

16956563069106188019…94889018090131379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.695 × 10⁹⁵(96-digit number)

16956563069106188019…94889018090131379201

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

3.391 × 10⁹⁵(96-digit number)

33913126138212376038…89778036180262758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.391 × 10⁹⁵(96-digit number)

33913126138212376038…89778036180262758401

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

6.782 × 10⁹⁵(96-digit number)

67826252276424752076…79556072360525516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.782 × 10⁹⁵(96-digit number)

67826252276424752076…79556072360525516801

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

1.356 × 10⁹⁶(97-digit number)

13565250455284950415…59112144721051033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.356 × 10⁹⁶(97-digit number)

13565250455284950415…59112144721051033601

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 #535,192

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