Block #428,672

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 6:35:38 AM · Difficulty 10.3432 · 6,387,548 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50dfe82586f897a7d1e6eda796ded3319d7de009f8b84780191351098fe31e46

View on Chainz ↗

Height

#428,672

Difficulty

10.343214

Transactions

Size

1.94 KB

Version

Bits

0a57dcda

Nonce

92,426

Timestamp

3/4/2014, 6:35:38 AM

Confirmations

6,387,548

Mined by

⛏️ aSt08AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

68da720a32b150d8db15b55d1a07d8b4430cd6a34b09dc3a3ea25b547a03235f

Transactions (2)

Coinbase24c6a5d4b60f4c…a02b47da1a5852

1 in → 22 out9.3300 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

a9c90042af0d50…c515c3f225c33b

5 in → 15 out46.6200 XPM1.07 KB

AJ7SsVUd…d5cfaxMN AatGF1Rk…wbQ98dWK AbQwTvfZ…nKz7USpN AZekxBFu…vTyGaSNV AGkgRwjw…hMugy5DS

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.

2.581 × 10⁹²(93-digit number)

25818367706598792892…51170463381099138399

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

2.581 × 10⁹²(93-digit number)

25818367706598792892…51170463381099138399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.581 × 10⁹²(93-digit number)

25818367706598792892…51170463381099138401

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

5.163 × 10⁹²(93-digit number)

51636735413197585785…02340926762198276799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.163 × 10⁹²(93-digit number)

51636735413197585785…02340926762198276801

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

1.032 × 10⁹³(94-digit number)

10327347082639517157…04681853524396553599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.032 × 10⁹³(94-digit number)

10327347082639517157…04681853524396553601

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

2.065 × 10⁹³(94-digit number)

20654694165279034314…09363707048793107199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.065 × 10⁹³(94-digit number)

20654694165279034314…09363707048793107201

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

4.130 × 10⁹³(94-digit number)

41309388330558068628…18727414097586214399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.130 × 10⁹³(94-digit number)

41309388330558068628…18727414097586214401

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 #428,672

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