Block #1,010,568

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2015, 9:34:52 PM · Difficulty 10.7257 · 5,794,441 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26e92f1ed49f970919550f3cbd9b41cc414fd6a79d667585828cafd3d9c0b8aa

View on Chainz ↗

Height

#1,010,568

Difficulty

10.725686

Transactions

Size

6.79 KB

Version

Bits

0ab9c687

Nonce

1,286,633,420

Timestamp

4/10/2015, 9:34:52 PM

Confirmations

5,794,441

Mined by

⛏️ P2SHALGnqDgmexYm2FMhPoHU4phM9Y955kLTFD

Merkle Root

0449eb6fa7c2f4064e17dc711c90a02e04028b2e766d09f88b017c46ab886d75

Transactions (5)

Coinbasebb9875087896b8…90b4800c171646

1 in → 1 out8.7600 XPM109 B

ALGnqDgm…955kLTFD

0a7b3a817f2783…1ce508eab436f5

1 in → 27 out120.3388 XPM1.05 KB

ARkWW3pZ…KZ8PC9ax AZBrM7td…t2Qv2X8y AXN8gcX8…e5ci2otR AMLbcJPE…FaBeUyLd AKtvwhAi…ZZfLBpiV

c39216a5d80e44…1b6070047c155e

1 in → 51 out94.2314 XPM1.85 KB

AYd4yStk…WAp5fkgN AcMgbMMN…5sUF3gjT AYJS19UR…SpwijnRf AVEKNxTX…UtGJpjqq AVsk7HkR…tcSCqHor

46968988975075…e5bbd77a044f4f

1 in → 51 out83.0049 XPM1.85 KB

AejcsRHy…X15pK4mH AKcnFUMd…GCYJkN3N AW2PKWB8…9yHTinyJ Aemy5QD9…6Mw3WzLh AUhLZdsR…gKMfjeDb

ccb5b3caa36fbc…3d050772b19c23

1 in → 51 out15.2095 XPM1.85 KB

AG7DRd78…Lhvirwcu AL9PkD7U…iXurtCLJ AMPuGPmo…Bh5yGMfq AdWwPseh…3jmSF9dw Ae81j9dF…Z8wPBUm6

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.

1.986 × 10⁹⁷(98-digit number)

19864002372859520313…84637671752342676479

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

1.986 × 10⁹⁷(98-digit number)

19864002372859520313…84637671752342676479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.986 × 10⁹⁷(98-digit number)

19864002372859520313…84637671752342676481

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

3.972 × 10⁹⁷(98-digit number)

39728004745719040626…69275343504685352959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.972 × 10⁹⁷(98-digit number)

39728004745719040626…69275343504685352961

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

7.945 × 10⁹⁷(98-digit number)

79456009491438081252…38550687009370705919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.945 × 10⁹⁷(98-digit number)

79456009491438081252…38550687009370705921

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

1.589 × 10⁹⁸(99-digit number)

15891201898287616250…77101374018741411839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.589 × 10⁹⁸(99-digit number)

15891201898287616250…77101374018741411841

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

3.178 × 10⁹⁸(99-digit number)

31782403796575232500…54202748037482823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.178 × 10⁹⁸(99-digit number)

31782403796575232500…54202748037482823681

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