Block #980,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2015, 6:26:56 PM · Difficulty 10.8474 · 5,826,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86c1491fd440f8f161babf4fac8e9ed903668f040192113009b91ddec3becba5

View on Chainz ↗

Height

#980,245

Difficulty

10.847428

Transactions

Size

1.07 KB

Version

Bits

0ad8f109

Nonce

4,630,008

Timestamp

3/18/2015, 6:26:56 PM

Confirmations

5,826,945

Mined by

⛏️ P2SHAJ7bmj6myCvj89gCvdCJ5H5xvu6XAYUkma

Merkle Root

e4ed654a88564edf2b16063631c5880ea9121a3b3108cca19a3b131fb0c19556

Transactions (3)

Coinbasef230c3863876fa…7db67ac9471aaf

1 in → 1 out8.5100 XPM109 B

AJ7bmj6m…6XAYUkma

68ba9fb6956223…21009be8b9504b

4 in → 2 out12.2000 XPM669 B

AbkSGfFy…rNGsN5he AQwjGQaw…vxuBy7tJ

fa8adb499c0964…02e55b8b5539fa

1 in → 2 out3.0172 XPM226 B

AG3TPGas…cJvesb2o AK7sfGnn…gfQNMjRz

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.

8.149 × 10⁹⁴(95-digit number)

81498591061529992932…69255459760047796559

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

8.149 × 10⁹⁴(95-digit number)

81498591061529992932…69255459760047796559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.149 × 10⁹⁴(95-digit number)

81498591061529992932…69255459760047796561

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

1.629 × 10⁹⁵(96-digit number)

16299718212305998586…38510919520095593119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.629 × 10⁹⁵(96-digit number)

16299718212305998586…38510919520095593121

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

3.259 × 10⁹⁵(96-digit number)

32599436424611997173…77021839040191186239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.259 × 10⁹⁵(96-digit number)

32599436424611997173…77021839040191186241

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

6.519 × 10⁹⁵(96-digit number)

65198872849223994346…54043678080382372479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.519 × 10⁹⁵(96-digit number)

65198872849223994346…54043678080382372481

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

1.303 × 10⁹⁶(97-digit number)

13039774569844798869…08087356160764744959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.303 × 10⁹⁶(97-digit number)

13039774569844798869…08087356160764744961

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 #980,245

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