Block #398,541

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 7:14:28 PM · Difficulty 10.4254 · 6,427,573 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9146d805a2c7a927ff27224e342a935f4705d3e645e273f4b7f37632d7247646

View on Chainz ↗

Height

#398,541

Difficulty

10.425437

Transactions

Size

1.15 KB

Version

Bits

0a6ce970

Nonce

41,756

Timestamp

2/10/2014, 7:14:28 PM

Confirmations

6,427,573

Mined by

⛏️ P2SHAHFWCKWQT8LyddsuRBgu53KwDFW7CD8T1C

Merkle Root

0128334f9c875e858609e0cd344b19d9e5da803abb83a94a36153c5318681f28

Transactions (4)

Coinbase6d4fa9e6f30d69…b491f29f4f093c

1 in → 1 out9.2200 XPM111 B

AHFWCKWQ…W7CD8T1C

95d0af59119448…b16c689e344782

1 in → 2 out5.1000 XPM227 B

AJcXvu4Y…D98xnnnU AM8sqZ7y…7QiacMzr

5c127fd71f051a…0d07442dbbb3df

1 in → 2 out4.0749 XPM225 B

APWt8PkL…TEASms6B AaTa1TJW…CS1ZqFKG

6798d35d64f183…e9fa25a7853066

3 in → 2 out1.0531 XPM522 B

AeY1Pqj7…kThM7BLv AaxcjPiT…Pq1Rq4uy

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.

5.495 × 10⁹⁵(96-digit number)

54958552027539224390…83587129360710896639

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

5.495 × 10⁹⁵(96-digit number)

54958552027539224390…83587129360710896639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.495 × 10⁹⁵(96-digit number)

54958552027539224390…83587129360710896641

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

1.099 × 10⁹⁶(97-digit number)

10991710405507844878…67174258721421793279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.099 × 10⁹⁶(97-digit number)

10991710405507844878…67174258721421793281

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

2.198 × 10⁹⁶(97-digit number)

21983420811015689756…34348517442843586559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.198 × 10⁹⁶(97-digit number)

21983420811015689756…34348517442843586561

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

4.396 × 10⁹⁶(97-digit number)

43966841622031379512…68697034885687173119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.396 × 10⁹⁶(97-digit number)

43966841622031379512…68697034885687173121

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

8.793 × 10⁹⁶(97-digit number)

87933683244062759025…37394069771374346239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.793 × 10⁹⁶(97-digit number)

87933683244062759025…37394069771374346241

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 #398,541

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