Block #369,914

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 5:31:28 PM · Difficulty 10.4477 · 6,446,922 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8da319cbb2060c68dee6ad7ec31dafde26b0254c758f63e90f40340f6f0ff8b6

View on Chainz ↗

Height

#369,914

Difficulty

10.447716

Transactions

Size

1.24 KB

Version

Bits

0a729d7d

Nonce

7,754

Timestamp

1/21/2014, 5:31:28 PM

Confirmations

6,446,922

Mined by

Ad6DSiVeK8WJiByqBqUcNefvpdnWiZdsG8

Merkle Root

5ef4fec32f8821081d0b0b587fd1ae194e90e8b5ba7ba33bc5ac2de2f85986c2

Transactions (2)

Coinbase457dcd2d3758a5…0c020f7a7b6906

1 in → 16 out9.1600 XPM607 B

Ad6DSiVe…nWiZdsG8 AW2fas42…gGAHYdHj AHg2Vvtk…kKAH15JW AUzEPJFG…kYkA5U9V AVFtsWuc…MYufD6Mw

8fd69cce926e94…aff0a6f4c8cabe

4 in → 2 out30.8508 XPM569 B

Abxhcsh1…kTin6L6a AT6vVdah…BJUnuBBz

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.

4.233 × 10⁹⁷(98-digit number)

42334103591784602447…74551853614962350079

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

4.233 × 10⁹⁷(98-digit number)

42334103591784602447…74551853614962350079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.233 × 10⁹⁷(98-digit number)

42334103591784602447…74551853614962350081

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

8.466 × 10⁹⁷(98-digit number)

84668207183569204895…49103707229924700159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.466 × 10⁹⁷(98-digit number)

84668207183569204895…49103707229924700161

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

1.693 × 10⁹⁸(99-digit number)

16933641436713840979…98207414459849400319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.693 × 10⁹⁸(99-digit number)

16933641436713840979…98207414459849400321

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

3.386 × 10⁹⁸(99-digit number)

33867282873427681958…96414828919698800639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.386 × 10⁹⁸(99-digit number)

33867282873427681958…96414828919698800641

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

6.773 × 10⁹⁸(99-digit number)

67734565746855363916…92829657839397601279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.773 × 10⁹⁸(99-digit number)

67734565746855363916…92829657839397601281

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 #369,914

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