Block #479,175

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 1:07:48 PM · Difficulty 10.5018 · 6,336,838 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4ed6734cafcc586f7526f00fff3023f669b7fd785348cb4509317690916191f0

View on Chainz ↗

Height

#479,175

Difficulty

10.501753

Transactions

Size

1.47 KB

Version

Bits

0a8072e9

Nonce

319,151

Timestamp

4/7/2014, 1:07:48 PM

Confirmations

6,336,838

Mined by

⛏️ O?AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

9c34ce573f815ed8f89b95afe76897143fc7aec8caf96b6f140a517c8b4ff269

Transactions (2)

Coinbase71f521a562024f…c8502f9fa7103b

1 in → 21 out9.0600 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb AZ34NcPy…8FPeFjPV AbPcCMg4…719q6mAX

ebe4aec10e1ab6…a84d063beedcbb

4 in → 1 out6.3814 XPM635 B

ATowQUod…EgwP4CAY

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.

7.981 × 10¹⁰⁰(101-digit number)

79816165966248286042…63800621329983009519

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

7.981 × 10¹⁰⁰(101-digit number)

79816165966248286042…63800621329983009519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.981 × 10¹⁰⁰(101-digit number)

79816165966248286042…63800621329983009521

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

1.596 × 10¹⁰¹(102-digit number)

15963233193249657208…27601242659966019039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.596 × 10¹⁰¹(102-digit number)

15963233193249657208…27601242659966019041

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

3.192 × 10¹⁰¹(102-digit number)

31926466386499314416…55202485319932038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.192 × 10¹⁰¹(102-digit number)

31926466386499314416…55202485319932038081

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

6.385 × 10¹⁰¹(102-digit number)

63852932772998628833…10404970639864076159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.385 × 10¹⁰¹(102-digit number)

63852932772998628833…10404970639864076161

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

1.277 × 10¹⁰²(103-digit number)

12770586554599725766…20809941279728152319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.277 × 10¹⁰²(103-digit number)

12770586554599725766…20809941279728152321

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 #479,175

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