Block #375,072

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 11:38:19 AM · Difficulty 10.4214 · 6,430,683 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33c814ad93137767bc026caf0b451ad32594e3dacedb1572383d0dbbc516ba12

View on Chainz ↗

Height

#375,072

Difficulty

10.421407

Transactions

Size

1.15 KB

Version

Bits

0a6be158

Nonce

426,101

Timestamp

1/25/2014, 11:38:19 AM

Confirmations

6,430,683

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2101c9189a6e01244cc89c2a1562f97776952b46df1970037ba2223252925ed8

Transactions (2)

Coinbase5bf689ba691f29…32d4a2f74a6f10

1 in → 20 out9.1900 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

93cff59203eee8…826a9febcf4ed8

2 in → 1 out997.9000 XPM340 B

ALzHpH4F…T1SsWfNc

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.

2.030 × 10⁹⁸(99-digit number)

20307202792181972316…20189904881479433919

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

2.030 × 10⁹⁸(99-digit number)

20307202792181972316…20189904881479433919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.030 × 10⁹⁸(99-digit number)

20307202792181972316…20189904881479433921

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

4.061 × 10⁹⁸(99-digit number)

40614405584363944633…40379809762958867839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.061 × 10⁹⁸(99-digit number)

40614405584363944633…40379809762958867841

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

8.122 × 10⁹⁸(99-digit number)

81228811168727889266…80759619525917735679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.122 × 10⁹⁸(99-digit number)

81228811168727889266…80759619525917735681

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

1.624 × 10⁹⁹(100-digit number)

16245762233745577853…61519239051835471359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.624 × 10⁹⁹(100-digit number)

16245762233745577853…61519239051835471361

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

3.249 × 10⁹⁹(100-digit number)

32491524467491155706…23038478103670942719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.249 × 10⁹⁹(100-digit number)

32491524467491155706…23038478103670942721

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