Block #403,647

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 7:46:06 AM · Difficulty 10.4314 · 6,399,378 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68a7c25b14f14715923c72b8f440b0a34bbdd57a73a018f0c4828d70ddc6cb8a

View on Chainz ↗

Height

#403,647

Difficulty

10.431386

Transactions

Size

2.01 KB

Version

Bits

0a6e6f4e

Nonce

Timestamp

2/14/2014, 7:46:06 AM

Confirmations

6,399,378

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

50de9b193ab424e7a9fa9b87b50ba8704874d05360a2a82a8d22e1226d9e54a7

Transactions (4)

Coinbase15a7a8e0a3f766…bfa4f1efdffa6b

1 in → 1 out9.2296 XPM116 B

AbwWkWZt…kawDhufa

09c8fc69af48b0…6b90c74aac6eea

4 in → 1 out4.2300 XPM637 B

AUoVSTnL…a7SUheaQ

4c9a9e94f9ce1a…ae47e81c29c1bf

5 in → 10 out27.8854 XPM987 B

AHYZdSXv…cJgrtqkY AeKNrjNj…1NEq95Ta AFyvtQwB…hQmBdnq5 ALAhD8Ug…hUBw662V AScSgvem…VqRbtmj4

3d5bd31f7c7389…ec85e5a4139e3c

1 in → 2 out3.0775 XPM226 B

AVSSoqRA…aFjFn3Zm AQkHwDaW…x1Pz4gEV

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.

2.947 × 10⁹²(93-digit number)

29473268873369750171…30113910896019043399

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

2.947 × 10⁹²(93-digit number)

29473268873369750171…30113910896019043399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.947 × 10⁹²(93-digit number)

29473268873369750171…30113910896019043401

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

5.894 × 10⁹²(93-digit number)

58946537746739500342…60227821792038086799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.894 × 10⁹²(93-digit number)

58946537746739500342…60227821792038086801

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

1.178 × 10⁹³(94-digit number)

11789307549347900068…20455643584076173599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.178 × 10⁹³(94-digit number)

11789307549347900068…20455643584076173601

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

2.357 × 10⁹³(94-digit number)

23578615098695800137…40911287168152347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.357 × 10⁹³(94-digit number)

23578615098695800137…40911287168152347201

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

4.715 × 10⁹³(94-digit number)

47157230197391600274…81822574336304694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.715 × 10⁹³(94-digit number)

47157230197391600274…81822574336304694401

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