Block #540,353

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/13/2014, 2:24:56 AM · Difficulty 10.9333 · 6,277,206 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef9e36815817c16e2632c9ece16e9e3dd1ea2d299adefed02231f399938d3d3f

View on Chainz ↗

Height

#540,353

Difficulty

10.933283

Transactions

Size

1.41 KB

Version

Bits

0aeeeba1

Nonce

265,869,143

Timestamp

5/13/2014, 2:24:56 AM

Confirmations

6,277,206

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5ffe5143edf019097ab517b966cce457a067adb7c84fc691a3f2df4d6cf970db

Transactions (4)

Coinbase4e9287e3c59eea…9a7335de0fe4f6

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

9851f8d378ab1c…2a3f32eca77b9b

4 in → 2 out33.1343 XPM670 B

AJofcPVi…KaTgbzFV AduENKr8…BWfVLdqn

098d9b8995bf9a…eecfa4166a577c

2 in → 2 out11.5900 XPM340 B

AMyFarm4…6npGvxsv AX948f6d…aizMp9T9

7d8a4525813849…340cbb4bbe9f43

1 in → 2 out1.1920 XPM226 B

ALg3koFT…9t3VmfrD AeZ53evZ…J9M3EfjE

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.

6.657 × 10⁹⁸(99-digit number)

66573206945652758615…23156207818550930879

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

6.657 × 10⁹⁸(99-digit number)

66573206945652758615…23156207818550930879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.657 × 10⁹⁸(99-digit number)

66573206945652758615…23156207818550930881

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

1.331 × 10⁹⁹(100-digit number)

13314641389130551723…46312415637101861759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.331 × 10⁹⁹(100-digit number)

13314641389130551723…46312415637101861761

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

2.662 × 10⁹⁹(100-digit number)

26629282778261103446…92624831274203723519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.662 × 10⁹⁹(100-digit number)

26629282778261103446…92624831274203723521

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

5.325 × 10⁹⁹(100-digit number)

53258565556522206892…85249662548407447039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.325 × 10⁹⁹(100-digit number)

53258565556522206892…85249662548407447041

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

1.065 × 10¹⁰⁰(101-digit number)

10651713111304441378…70499325096814894079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.065 × 10¹⁰⁰(101-digit number)

10651713111304441378…70499325096814894081

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 #540,353

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