Block #300,406

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 2:03:10 PM · Difficulty 9.9923 · 6,507,954 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16a282bdc6d0bf75f1788757a0cb76e49c2d832410ef26ee27078d465721529c

View on Chainz ↗

Height

#300,406

Difficulty

9.992279

Transactions

Size

19.67 KB

Version

Bits

09fe0602

Nonce

225,304

Timestamp

12/8/2013, 2:03:10 PM

Confirmations

6,507,954

Mined by

⛏️ vaR{Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

42a5f654bdfb25d845b896daa5382d0167f26eb6325310b05008ff7e09a70a83

Transactions (4)

Coinbase96fdc241ed90ad…cf5854a42b0323

1 in → 28 out9.9800 XPM1015 B

Ad9pSzHt…cpJ3y2zz AWA5FEzr…x9RdPKTy AQf7sjuh…sNY5fXpu APeshfYV…3PKcKMKH AT1xr4ZB…3dcDkfYg

4ed6c020d49de1…f0bcf975c77548

1 in → 2 out3775.4586 XPM227 B

AZiK2HU5…peWLqXp4 Ad4v7RFH…uAbdLUwX

a8a2fdec09a5dd…9c7a9d391d1126

125 in → 2 out41.0387 XPM18.14 KB

ASbpg6Gh…smgfZTSf ALxm8Yya…1FETv18e

70a191e3b7a7b7…7ec8390eb3d789

1 in → 2 out1.9515 XPM225 B

AP9zKd6o…Fi9vxXuF AVvyhacf…VgfUiyaR

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.

2.109 × 10⁹⁶(97-digit number)

21098427658251548240…98994984054078148799

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

2.109 × 10⁹⁶(97-digit number)

21098427658251548240…98994984054078148799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.109 × 10⁹⁶(97-digit number)

21098427658251548240…98994984054078148801

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

4.219 × 10⁹⁶(97-digit number)

42196855316503096480…97989968108156297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.219 × 10⁹⁶(97-digit number)

42196855316503096480…97989968108156297601

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

8.439 × 10⁹⁶(97-digit number)

84393710633006192961…95979936216312595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.439 × 10⁹⁶(97-digit number)

84393710633006192961…95979936216312595201

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

1.687 × 10⁹⁷(98-digit number)

16878742126601238592…91959872432625190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.687 × 10⁹⁷(98-digit number)

16878742126601238592…91959872432625190401

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

3.375 × 10⁹⁷(98-digit number)

33757484253202477184…83919744865250380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.375 × 10⁹⁷(98-digit number)

33757484253202477184…83919744865250380801

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

Block #300,406

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