Block #446,348

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 12:05:41 PM · Difficulty 10.3622 · 6,353,094 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58a1e162b31fee742d45e6d00a5b1717d2f8964b09a23fa5026849680b408923

View on Chainz ↗

Height

#446,348

Difficulty

10.362186

Transactions

Size

4.67 KB

Version

Bits

0a5cb835

Nonce

3,801,328

Timestamp

3/16/2014, 12:05:41 PM

Confirmations

6,353,094

Mined by

⛏️ P2SHAPwskzim5qRcVJJ62z97pt1wbiPbWuLu2X

Merkle Root

d241e0afceb5709c30a6060d5af2c1028316b87edf1cfcd8d5751eb2be1048d9

Transactions (4)

Coinbase96c4f16bb26359…cf2fecd4ecaee3

1 in → 1 out9.3600 XPM110 B

APwskzim…PbWuLu2X

e6cee0f42f857d…4ca2676a0d4e90

4 in → 12 out37.3100 XPM874 B

AFuWmgaK…VU6dnSgw AYSwRnwG…4im2Y9vG AeMG3MbB…Yn1ndGmN AeKNrjNj…1NEq95Ta AZXpgixf…Qe5FqFEz

af4e02011d9836…774d2030e32578

23 in → 2 out13.1897 XPM3.40 KB

Ae15418y…NN5bVKkm AYCJ8hVg…ANw1X1TB

261aff3b057f5e…09debe91b4bbd4

1 in → 2 out1.2039 XPM225 B

AX552jX9…gDRZgjsX AYaToAH4…KKdiq63H

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.

4.057 × 10⁹⁶(97-digit number)

40572781468300616205…96929140269569638399

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

4.057 × 10⁹⁶(97-digit number)

40572781468300616205…96929140269569638399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.057 × 10⁹⁶(97-digit number)

40572781468300616205…96929140269569638401

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

8.114 × 10⁹⁶(97-digit number)

81145562936601232411…93858280539139276799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.114 × 10⁹⁶(97-digit number)

81145562936601232411…93858280539139276801

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

1.622 × 10⁹⁷(98-digit number)

16229112587320246482…87716561078278553599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.622 × 10⁹⁷(98-digit number)

16229112587320246482…87716561078278553601

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

3.245 × 10⁹⁷(98-digit number)

32458225174640492964…75433122156557107199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.245 × 10⁹⁷(98-digit number)

32458225174640492964…75433122156557107201

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

6.491 × 10⁹⁷(98-digit number)

64916450349280985929…50866244313114214399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.491 × 10⁹⁷(98-digit number)

64916450349280985929…50866244313114214401

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