Block #278,388

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 11:20:11 PM · Difficulty 9.9688 · 6,525,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b456aa9e2aee6d29837bfd127be0e18a502916986692b0ad2cbebc9440ffe8fd

View on Chainz ↗

Height

#278,388

Difficulty

9.968798

Transactions

Size

1.65 KB

Version

Bits

09f80327

Nonce

3,691

Timestamp

11/27/2013, 11:20:11 PM

Confirmations

6,525,107

Mined by

⛏️ P2SHAHH6RVE7YTEuTdnQN3mxJ2bg17XbTVjUJC

Merkle Root

45e2ff20ecf9f9b8c98a40f70934bdaf85083595d8bcfd6c29f2a8e1b289ef9a

Transactions (5)

Coinbasede0f83ba6fd4aa…3766c9eb1e5a83

1 in → 1 out10.0900 XPM109 B

AHH6RVE7…XbTVjUJC

6767af52cda85a…af971aad5d4a4f

1 in → 2 out200.3268 XPM226 B

AcnbGTua…7Hm3hWSR AS6JTotm…mC4Z9q5b

b3cbea307f352e…d24883ca331285

5 in → 2 out10.0307 XPM816 B

AeKVMi7g…fgD8Bne2 AZQ6UPYd…vtKVGM8z

5fb5a415c0e687…8b2f9ee2ac72fc

1 in → 2 out5.9866 XPM226 B

AT2fg9QX…2cmojDuy AQpRzzDz…PeodSkXe

7395782f3aa37e…0e8f5d5aff0a4e

1 in → 2 out4.8745 XPM225 B

ARYJiGcH…7eaSxdkL Ac5P6b6v…d3HZGz6B

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.

3.810 × 10⁹⁰(91-digit number)

38109652727239202370…36763706641995720879

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

3.810 × 10⁹⁰(91-digit number)

38109652727239202370…36763706641995720879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.810 × 10⁹⁰(91-digit number)

38109652727239202370…36763706641995720881

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

7.621 × 10⁹⁰(91-digit number)

76219305454478404741…73527413283991441759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.621 × 10⁹⁰(91-digit number)

76219305454478404741…73527413283991441761

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

1.524 × 10⁹¹(92-digit number)

15243861090895680948…47054826567982883519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.524 × 10⁹¹(92-digit number)

15243861090895680948…47054826567982883521

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

3.048 × 10⁹¹(92-digit number)

30487722181791361896…94109653135965767039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.048 × 10⁹¹(92-digit number)

30487722181791361896…94109653135965767041

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

6.097 × 10⁹¹(92-digit number)

60975444363582723792…88219306271931534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.097 × 10⁹¹(92-digit number)

60975444363582723792…88219306271931534081

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