Block #496,659

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 5:03:53 AM · Difficulty 10.7572 · 6,314,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6caece80befd2ef38b6a7f197006c94c16d8a299035e9e6861517ec0fb71b0ba

View on Chainz ↗

Height

#496,659

Difficulty

10.757200

Transactions

Size

1.08 KB

Version

Bits

0ac1d7e0

Nonce

182,593,206

Timestamp

4/17/2014, 5:03:53 AM

Confirmations

6,314,430

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7c88bf2c9d4d50b45991e6e957e28302dff102cc51a21def1486909bc7c7375c

Transactions (3)

Coinbasede849f15267189…6800b0500ca816

1 in → 1 out8.6500 XPM116 B

AbwWkWZt…kawDhufa

f0b593ce917395…f6e988588366f7

4 in → 2 out4.0485 XPM670 B

ASdqd5Qu…1F8KZYNX AZSjhnMj…Mnf3y9ki

0aff653e64e90b…cdaca0d5e5281e

1 in → 2 out4.0686 XPM226 B

AVmAYjtz…Cn5X1bXD AcP8jseU…hwvN422m

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.

6.729 × 10⁹⁹(100-digit number)

67295599018835333631…93300481188150527999

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

6.729 × 10⁹⁹(100-digit number)

67295599018835333631…93300481188150527999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.729 × 10⁹⁹(100-digit number)

67295599018835333631…93300481188150528001

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

1.345 × 10¹⁰⁰(101-digit number)

13459119803767066726…86600962376301055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.345 × 10¹⁰⁰(101-digit number)

13459119803767066726…86600962376301056001

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

2.691 × 10¹⁰⁰(101-digit number)

26918239607534133452…73201924752602111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.691 × 10¹⁰⁰(101-digit number)

26918239607534133452…73201924752602112001

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

5.383 × 10¹⁰⁰(101-digit number)

53836479215068266904…46403849505204223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.383 × 10¹⁰⁰(101-digit number)

53836479215068266904…46403849505204224001

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

1.076 × 10¹⁰¹(102-digit number)

10767295843013653380…92807699010408447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.076 × 10¹⁰¹(102-digit number)

10767295843013653380…92807699010408448001

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 #496,659

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