Block #966,976

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2015, 12:11:11 AM · Difficulty 10.8259 · 5,859,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a6ed987d21f18a990c3d0eaa0c41da8903961adc0a8eae177ce2cacd3379ca7

View on Chainz ↗

Height

#966,976

Difficulty

10.825872

Transactions

Size

1.28 KB

Version

Bits

0ad36c52

Nonce

450,044,150

Timestamp

3/10/2015, 12:11:11 AM

Confirmations

5,859,945

Mined by

⛏️ P2SHALdF1aU3bSWDJADgfwTySD9UvHQ4Xx7e2u

Merkle Root

60f675918b9e54d98edee7988765dcd4785997aaedc25eaf1dc10e39fdc5f816

Transactions (2)

Coinbasef3458cde0576a8…35526de70b10fa

1 in → 1 out8.5400 XPM110 B

ALdF1aU3…Q4Xx7e2u

c74dd1e73a915c…d66296cd09e49f

7 in → 2 out8.6967 XPM1.09 KB

AQuxwNQx…XzfiDSCq AHpzP6SN…JEHaDu4e

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.

2.146 × 10⁹⁶(97-digit number)

21465146898304314105…54528687078557383679

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

2.146 × 10⁹⁶(97-digit number)

21465146898304314105…54528687078557383679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.146 × 10⁹⁶(97-digit number)

21465146898304314105…54528687078557383681

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

4.293 × 10⁹⁶(97-digit number)

42930293796608628211…09057374157114767359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.293 × 10⁹⁶(97-digit number)

42930293796608628211…09057374157114767361

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

8.586 × 10⁹⁶(97-digit number)

85860587593217256422…18114748314229534719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.586 × 10⁹⁶(97-digit number)

85860587593217256422…18114748314229534721

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

1.717 × 10⁹⁷(98-digit number)

17172117518643451284…36229496628459069439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.717 × 10⁹⁷(98-digit number)

17172117518643451284…36229496628459069441

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

3.434 × 10⁹⁷(98-digit number)

34344235037286902568…72458993256918138879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.434 × 10⁹⁷(98-digit number)

34344235037286902568…72458993256918138881

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 #966,976

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