Block #989,368

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/24/2015, 11:35:33 PM · Difficulty 10.8529 · 5,813,427 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

260b2172893d63607c2d07f36e4542578da08870f2b50522323499a2e443786d

View on Chainz ↗

Height

#989,368

Difficulty

10.852938

Transactions

Size

4.11 KB

Version

Bits

0ada5a2a

Nonce

43,371,363

Timestamp

3/24/2015, 11:35:33 PM

Confirmations

5,813,427

Mined by

⛏️ P2SHAXXvh6rYRt46ngypu2KXcAc2xxSetCRejn

Merkle Root

1af99cb305cf1b47b02a9be51829c42a9c8831423aaf7da01d35ad315f0f66c1

Transactions (4)

Coinbase839f70e1a8e2a3…d48abe537c35be

1 in → 1 out8.5300 XPM109 B

AXXvh6rY…SetCRejn

a756edbdb599f0…e858da9aba05e9

1 in → 51 out22.2121 XPM1.85 KB

Abjyq3vY…eLpKKXCc AaVTBaH5…XU1JJ57s APM3RoGj…Vb6frVuB AZHRhjg9…scMau2cC ARbmELZZ…D2EmA9eK

7129739e74c3e2…97c97d6e3fde39

1 in → 51 out50.8160 XPM1.85 KB

AVZv3esg…CSnqAJyB AP964WgM…L2oX7Eow AGLZyE6z…Bf5NJteP AHVUZkSm…nsGHqndk AbHkvZK4…jdF6E75T

1b961035201d9e…80a43e22957520

1 in → 2 out6.3567 XPM225 B

Af3aPj7K…cnGd5dnY AHbceGQc…pmFJ5Dj6

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.

1.692 × 10⁹⁵(96-digit number)

16927757474244934180…53551112854879109119

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

1.692 × 10⁹⁵(96-digit number)

16927757474244934180…53551112854879109119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.692 × 10⁹⁵(96-digit number)

16927757474244934180…53551112854879109121

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

3.385 × 10⁹⁵(96-digit number)

33855514948489868361…07102225709758218239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.385 × 10⁹⁵(96-digit number)

33855514948489868361…07102225709758218241

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

6.771 × 10⁹⁵(96-digit number)

67711029896979736723…14204451419516436479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.771 × 10⁹⁵(96-digit number)

67711029896979736723…14204451419516436481

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

1.354 × 10⁹⁶(97-digit number)

13542205979395947344…28408902839032872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.354 × 10⁹⁶(97-digit number)

13542205979395947344…28408902839032872961

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

2.708 × 10⁹⁶(97-digit number)

27084411958791894689…56817805678065745919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.708 × 10⁹⁶(97-digit number)

27084411958791894689…56817805678065745921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.416 × 10⁹⁶(97-digit number)

54168823917583789378…13635611356131491839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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