Block #2,641,950

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 1:16:32 PM · Difficulty 11.6376 · 4,194,742 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b8fc95d508771df3eece804daee08bd3b4edb678e5eee6fd25530e14583f9aa

View on Chainz ↗

Height

#2,641,950

Difficulty

11.637557

Transactions

Size

1.15 KB

Version

Bits

0ba336ef

Nonce

78,518,014

Timestamp

5/1/2018, 1:16:32 PM

Confirmations

4,194,742

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

93205ff87cfab75542cf2ae5a39e9fd41337d28f8f75adba790612e0ddf12d8d

Transactions (3)

Coinbase8b05873325b4c7…d69aad1e095124

1 in → 1 out7.3900 XPM110 B

Adqah8zh…1WwoHJ9t

3c9e1818282d50…20a3823ffd7715

3 in → 2 out19.0729 XPM453 B

ASJPMMHp…S3mJn5SK ANWdJ2nc…BW7RisDk

a6217c3cd4d5d7…d5229a392a874a

3 in → 2 out2.0292 XPM524 B

AYrVVyHX…izr1k7kM AbpSXkao…ETqhD2oz

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.

4.203 × 10⁹⁷(98-digit number)

42030944187709881125…16933448123588935679

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

4.203 × 10⁹⁷(98-digit number)

42030944187709881125…16933448123588935679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.203 × 10⁹⁷(98-digit number)

42030944187709881125…16933448123588935681

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

8.406 × 10⁹⁷(98-digit number)

84061888375419762250…33866896247177871359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.406 × 10⁹⁷(98-digit number)

84061888375419762250…33866896247177871361

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

1.681 × 10⁹⁸(99-digit number)

16812377675083952450…67733792494355742719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.681 × 10⁹⁸(99-digit number)

16812377675083952450…67733792494355742721

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

3.362 × 10⁹⁸(99-digit number)

33624755350167904900…35467584988711485439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.362 × 10⁹⁸(99-digit number)

33624755350167904900…35467584988711485441

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

6.724 × 10⁹⁸(99-digit number)

67249510700335809800…70935169977422970879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.724 × 10⁹⁸(99-digit number)

67249510700335809800…70935169977422970881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.344 × 10⁹⁹(100-digit number)

13449902140067161960…41870339954845941759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,641,950

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