Block #397,760

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 7:26:10 AM · Difficulty 10.4167 · 6,398,072 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0336838e79de6a204a6e41db168df0debdc8c8012483e80804a59164f5802144

View on Chainz ↗

Height

#397,760

Difficulty

10.416743

Transactions

Size

865 B

Version

Bits

0a6aafaa

Nonce

69,429

Timestamp

2/10/2014, 7:26:10 AM

Confirmations

6,398,072

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

feecc5efebf255320e9649367786e5451797913cb1a730e0e7acf5d1df480717

Transactions (2)

Coinbaseb7076a07d745e7…1301d631883c0c

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

9bc782ea904911…1a96182bee640b

3 in → 9 out27.5900 XPM658 B

AVE94w5J…WN4TXnY3 AcpjiZSC…TNRJHCGa AL6hfYqf…jYfKt9LA ALNTdrTH…hyfEy639 AUDA3a2M…mDChw1vJ

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.

2.252 × 10⁹⁷(98-digit number)

22523149184378788766…65268847381691914669

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

2.252 × 10⁹⁷(98-digit number)

22523149184378788766…65268847381691914669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.252 × 10⁹⁷(98-digit number)

22523149184378788766…65268847381691914671

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

4.504 × 10⁹⁷(98-digit number)

45046298368757577532…30537694763383829339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.504 × 10⁹⁷(98-digit number)

45046298368757577532…30537694763383829341

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

9.009 × 10⁹⁷(98-digit number)

90092596737515155064…61075389526767658679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.009 × 10⁹⁷(98-digit number)

90092596737515155064…61075389526767658681

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

1.801 × 10⁹⁸(99-digit number)

18018519347503031012…22150779053535317359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.801 × 10⁹⁸(99-digit number)

18018519347503031012…22150779053535317361

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

3.603 × 10⁹⁸(99-digit number)

36037038695006062025…44301558107070634719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.603 × 10⁹⁸(99-digit number)

36037038695006062025…44301558107070634721

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