Block #442,839

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 3:37:11 AM · Difficulty 10.3442 · 6,367,505 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

028f681bc74acb713271295b07185678c56a1c115bf4e5c8ec3d96eb60e27579

View on Chainz ↗

Height

#442,839

Difficulty

10.344247

Transactions

Size

1.37 KB

Version

Bits

0a582098

Nonce

29,322

Timestamp

3/14/2014, 3:37:11 AM

Confirmations

6,367,505

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

768c5a472a4ca9f78c2d5135fde63a8cdc134e549c4eb7aba04799499ea1a536

Transactions (5)

Coinbase2c76c6cefda62c…1bab4b8ce2d983

1 in → 1 out9.3700 XPM116 B

AbwWkWZt…kawDhufa

71871cfbe0a667…d2b0522a54616b

3 in → 2 out1317.2478 XPM523 B

AXCtNygQ…76nRNgdf AdbHwMhD…BrWZDcw5

f82db6cc5c5bbe…a2c6f346fcb9ec

1 in → 2 out6.1538 XPM226 B

AViGNKhn…R8HAjVai AYXknZxW…fganXV4Z

b82c13d242370a…0396637e70e32f

1 in → 2 out2.6873 XPM225 B

Ac5Zs4YY…USMWm5xJ AZLeZVok…mBLmxEiM

13de550fafce54…19099d5ea0b120

1 in → 2 out1.6632 XPM226 B

AevNDWMA…S9ZqoSDw AYx4nLzA…D9yE3Min

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.

2.200 × 10⁹⁷(98-digit number)

22003713154230223399…57886650870298221039

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

2.200 × 10⁹⁷(98-digit number)

22003713154230223399…57886650870298221039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.200 × 10⁹⁷(98-digit number)

22003713154230223399…57886650870298221041

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

4.400 × 10⁹⁷(98-digit number)

44007426308460446799…15773301740596442079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.400 × 10⁹⁷(98-digit number)

44007426308460446799…15773301740596442081

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

8.801 × 10⁹⁷(98-digit number)

88014852616920893598…31546603481192884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.801 × 10⁹⁷(98-digit number)

88014852616920893598…31546603481192884161

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

1.760 × 10⁹⁸(99-digit number)

17602970523384178719…63093206962385768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.760 × 10⁹⁸(99-digit number)

17602970523384178719…63093206962385768321

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

3.520 × 10⁹⁸(99-digit number)

35205941046768357439…26186413924771536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.520 × 10⁹⁸(99-digit number)

35205941046768357439…26186413924771536641

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 #442,839

Cookie Preferences