Block #296,649

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 3:41:03 AM · Difficulty 9.9918 · 6,529,021 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7504375a34579c64a14ee5902011ef5b8e4af7b795fc607b14dea5a03ecd66bc

View on Chainz ↗

Height

#296,649

Difficulty

9.991754

Transactions

Size

1.18 KB

Version

Bits

09fde39d

Nonce

1,439

Timestamp

12/6/2013, 3:41:03 AM

Confirmations

6,529,021

Mined by

⛏️ aRFAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

a054cbbedc4f3caa8fdcf26ae919ce4ca3ffa973391a4c947487e6016de66275

Transactions (1)

Coinbasea054cbbedc4f3c…87e6016de66275

1 in → 31 out9.9800 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AJzWx2VD…j4ZSMit5 AJuoT41d…z62Tj7WM AUpEhJju…7ou9xH7C

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.

4.689 × 10⁹⁴(95-digit number)

46892690876026322027…13749914220493029749

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

4.689 × 10⁹⁴(95-digit number)

46892690876026322027…13749914220493029749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.689 × 10⁹⁴(95-digit number)

46892690876026322027…13749914220493029751

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

9.378 × 10⁹⁴(95-digit number)

93785381752052644055…27499828440986059499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.378 × 10⁹⁴(95-digit number)

93785381752052644055…27499828440986059501

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

1.875 × 10⁹⁵(96-digit number)

18757076350410528811…54999656881972118999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.875 × 10⁹⁵(96-digit number)

18757076350410528811…54999656881972119001

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

3.751 × 10⁹⁵(96-digit number)

37514152700821057622…09999313763944237999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.751 × 10⁹⁵(96-digit number)

37514152700821057622…09999313763944238001

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

7.502 × 10⁹⁵(96-digit number)

75028305401642115244…19998627527888475999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.502 × 10⁹⁵(96-digit number)

75028305401642115244…19998627527888476001

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 #296,649

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