Block #411,563

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 8:58:19 PM · Difficulty 10.4267 · 6,393,797 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

755b2bb0dd82026a4a4293fca34ff80f6823daa7d09f870cd0ddd8516f19f82d

View on Chainz ↗

Height

#411,563

Difficulty

10.426717

Transactions

Size

2.29 KB

Version

Bits

0a6d3d4c

Nonce

1,991

Timestamp

2/19/2014, 8:58:19 PM

Confirmations

6,393,797

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

df62044d98fde16c458ba91397c06718b6fb454fdb23b7790a7d51764b460853

Transactions (5)

Coinbasea82c4ba142837e…2572b185bc5320

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

769e5eaf682d82…3fa9f9127a9fc2

4 in → 2 out633.0950 XPM668 B

AKB6AwpP…jckKfvmU AXv5Vsmg…cUo8RWS1

b01954a6edf07c…b5e09b122b5a5e

2 in → 2 out13.3241 XPM374 B

AJJu16ii…1zZTWnqc AVBEGTi2…NxA1WAUh

a3f1e64d8157ad…c0664945da4ec0

4 in → 12 out36.8400 XPM872 B

AYZGcg17…JGywZzmz AY9tgoA9…kkkXTaFe AT8akpZ5…X48Kza4D ATqL92FR…hv5XHEu1 AG9LVB24…j5abSW7c

71587024484c1f…2d7c51d2fe6269

1 in → 2 out6.0353 XPM226 B

AN8zbbcx…temocTh9 AN4ZJKxe…oBDtmr63

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.

3.995 × 10⁹⁷(98-digit number)

39954639993279866090…33041522457337838949

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

3.995 × 10⁹⁷(98-digit number)

39954639993279866090…33041522457337838949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.995 × 10⁹⁷(98-digit number)

39954639993279866090…33041522457337838951

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

7.990 × 10⁹⁷(98-digit number)

79909279986559732181…66083044914675677899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.990 × 10⁹⁷(98-digit number)

79909279986559732181…66083044914675677901

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

1.598 × 10⁹⁸(99-digit number)

15981855997311946436…32166089829351355799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.598 × 10⁹⁸(99-digit number)

15981855997311946436…32166089829351355801

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

3.196 × 10⁹⁸(99-digit number)

31963711994623892872…64332179658702711599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.196 × 10⁹⁸(99-digit number)

31963711994623892872…64332179658702711601

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

6.392 × 10⁹⁸(99-digit number)

63927423989247785745…28664359317405423199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.392 × 10⁹⁸(99-digit number)

63927423989247785745…28664359317405423201

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