Block #409,192

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 5:35:49 AM · Difficulty 10.4240 · 6,405,837 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf6d82e87ba0e3fd1638ffc14cd82f4e4dd5492ab7f949f680d79be0b65a7dba

View on Chainz ↗

Height

#409,192

Difficulty

10.424038

Transactions

Size

1.38 KB

Version

Bits

0a6c8db9

Nonce

26,384

Timestamp

2/18/2014, 5:35:49 AM

Confirmations

6,405,837

Mined by

⛏️ h>aS8AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

da4e5d8c1d6ade568cc744a7a5bcd9c062c9fed2c7f9b8d82798624927716d5d

Transactions (2)

Coinbased31c1d5d80a9cc…29936dc0c4858d

1 in → 17 out9.1900 XPM641 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

7a6398b50baf20…308cf4fec8b6d7

5 in → 2 out37.0110 XPM680 B

AJbq7Mk7…NKwRjJLP AUh22Rvr…RptGggF5

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.

1.055 × 10¹⁰⁰(101-digit number)

10557179660539319848…76655618655773794009

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

1.055 × 10¹⁰⁰(101-digit number)

10557179660539319848…76655618655773794009

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.055 × 10¹⁰⁰(101-digit number)

10557179660539319848…76655618655773794011

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

2.111 × 10¹⁰⁰(101-digit number)

21114359321078639697…53311237311547588019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.111 × 10¹⁰⁰(101-digit number)

21114359321078639697…53311237311547588021

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

4.222 × 10¹⁰⁰(101-digit number)

42228718642157279394…06622474623095176039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.222 × 10¹⁰⁰(101-digit number)

42228718642157279394…06622474623095176041

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

8.445 × 10¹⁰⁰(101-digit number)

84457437284314558789…13244949246190352079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.445 × 10¹⁰⁰(101-digit number)

84457437284314558789…13244949246190352081

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

1.689 × 10¹⁰¹(102-digit number)

16891487456862911757…26489898492380704159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.689 × 10¹⁰¹(102-digit number)

16891487456862911757…26489898492380704161

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 #409,192

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