Block #403,081

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 9:46:58 PM · Difficulty 10.4353 · 6,404,853 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d062e3873bfc4bac6b8a1aea0bdb8dff2d92f2c4988a4556198598f2c7922c9c

View on Chainz ↗

Height

#403,081

Difficulty

10.435262

Transactions

Size

1.41 KB

Version

Bits

0a6f6d59

Nonce

21,406

Timestamp

2/13/2014, 9:46:58 PM

Confirmations

6,404,853

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

25fec1d4fd39223613032f2ac7a9c8b78f9af373a841861ff56b5bad28dd79db

Transactions (4)

Coinbase26d3f783bbcd39…082af8d0d6c85d

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

96f3004a515809…aac9db0fca9451

5 in → 2 out372.1877 XPM818 B

AXsUbc4c…4bXeaZQN ATMoSzLo…AWXrTMZC

808c6fee6eec19…b291909ed30285

1 in → 2 out1.8988 XPM225 B

ANX7pJYQ…8mMtrx5q AafXBxi8…MTbj7rvU

2b14db949f69f2…ed8813792e121d

1 in → 1 out0.0385 XPM192 B

AS4CfFYA…ksiezrwM

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.

5.415 × 10¹⁰⁰(101-digit number)

54153055573150072980…03300878658912747519

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

5.415 × 10¹⁰⁰(101-digit number)

54153055573150072980…03300878658912747519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.415 × 10¹⁰⁰(101-digit number)

54153055573150072980…03300878658912747521

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

1.083 × 10¹⁰¹(102-digit number)

10830611114630014596…06601757317825495039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.083 × 10¹⁰¹(102-digit number)

10830611114630014596…06601757317825495041

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

2.166 × 10¹⁰¹(102-digit number)

21661222229260029192…13203514635650990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.166 × 10¹⁰¹(102-digit number)

21661222229260029192…13203514635650990081

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

4.332 × 10¹⁰¹(102-digit number)

43322444458520058384…26407029271301980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.332 × 10¹⁰¹(102-digit number)

43322444458520058384…26407029271301980161

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

8.664 × 10¹⁰¹(102-digit number)

86644888917040116769…52814058542603960319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.664 × 10¹⁰¹(102-digit number)

86644888917040116769…52814058542603960321

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 #403,081

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