Block #399,436

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 10:27:12 AM · Difficulty 10.4240 · 6,405,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

656c4582b5ca72cfece39844dac4000c682a202710a3d7d859f082e432387695

View on Chainz ↗

Height

#399,436

Difficulty

10.424038

Transactions

Size

1.89 KB

Version

Bits

0a6c8dc6

Nonce

22,746

Timestamp

2/11/2014, 10:27:12 AM

Confirmations

6,405,651

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a14d42f890e017ae01f25c4a3c82b2a47e1a5798fb07b8e19731a3e0c271fec4

Transactions (3)

Coinbase5504df601a4f5e…382977b6bcb7db

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

1fd340b6914677…1e456ff25bc4eb

1 in → 2 out9.1900 XPM227 B

AWP2TX3f…JKXpoiL7 AP1SXPi4…TwuAMW7o

e9b19c0e433e85…e74adc6c877a7d

8 in → 13 out38.1482 XPM1.46 KB

ANfx3fUc…19v4zb54 AJsjfvkf…xm2ix6cD AFmv5mWD…urvyngVQ ALzeejWz…d7byrHth ANqJPxk9…rKume2u6

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.

7.121 × 10⁹⁵(96-digit number)

71217187896117928172…92944854683211262559

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

7.121 × 10⁹⁵(96-digit number)

71217187896117928172…92944854683211262559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.121 × 10⁹⁵(96-digit number)

71217187896117928172…92944854683211262561

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

1.424 × 10⁹⁶(97-digit number)

14243437579223585634…85889709366422525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.424 × 10⁹⁶(97-digit number)

14243437579223585634…85889709366422525121

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

2.848 × 10⁹⁶(97-digit number)

28486875158447171268…71779418732845050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.848 × 10⁹⁶(97-digit number)

28486875158447171268…71779418732845050241

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

5.697 × 10⁹⁶(97-digit number)

56973750316894342537…43558837465690100479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.697 × 10⁹⁶(97-digit number)

56973750316894342537…43558837465690100481

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

1.139 × 10⁹⁷(98-digit number)

11394750063378868507…87117674931380200959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.139 × 10⁹⁷(98-digit number)

11394750063378868507…87117674931380200961

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