Block #340,498

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 7:55:05 PM · Difficulty 10.1331 · 6,458,864 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc991c81db4abc9794c6aacf97b50eee4897b396b4be351ead2556546c08c27c

View on Chainz ↗

Height

#340,498

Difficulty

10.133142

Transactions

Size

1.79 KB

Version

Bits

0a22159b

Nonce

76,050

Timestamp

1/2/2014, 7:55:05 PM

Confirmations

6,458,864

Mined by

⛏️ 2aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

dbc8715bd62c695cf0b3bb3a28cbdc2fca6fcbb2d87ee35bf3cf15d3eeca47f1

Transactions (4)

Coinbasec727f1c2b664a9…bdabf22c5ecc16

1 in → 27 out9.7200 XPM981 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 AG5YAjec…VhA4Aeh1 AM1wsdX3…NqVu85hE

96d94d923e666d…1d57b688ac8031

2 in → 1 out6.1137 XPM340 B

AHH1yb5V…LtoPhaGJ

94898d7f62d1af…34baae4f34cd48

1 in → 1 out0.8900 XPM193 B

ATzNqULc…5WQcwDbE

78bf9e590fb62e…ead30d1a809155

1 in → 2 out6.4659 XPM227 B

AZFHWFZn…ZsTRDT7R Ac5jsLZ1…sXVHcquW

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.

4.039 × 10¹⁰⁰(101-digit number)

40398900234053681826…68072787264401890999

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

4.039 × 10¹⁰⁰(101-digit number)

40398900234053681826…68072787264401890999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.039 × 10¹⁰⁰(101-digit number)

40398900234053681826…68072787264401891001

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

8.079 × 10¹⁰⁰(101-digit number)

80797800468107363652…36145574528803781999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.079 × 10¹⁰⁰(101-digit number)

80797800468107363652…36145574528803782001

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

1.615 × 10¹⁰¹(102-digit number)

16159560093621472730…72291149057607563999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.615 × 10¹⁰¹(102-digit number)

16159560093621472730…72291149057607564001

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

3.231 × 10¹⁰¹(102-digit number)

32319120187242945460…44582298115215127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.231 × 10¹⁰¹(102-digit number)

32319120187242945460…44582298115215128001

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

6.463 × 10¹⁰¹(102-digit number)

64638240374485890921…89164596230430255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.463 × 10¹⁰¹(102-digit number)

64638240374485890921…89164596230430256001

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