Block #284,058

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 11:55:07 PM · Difficulty 9.9821 · 6,515,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a76d204aa2f060c4966826db18a09104a5457f5b947a7d833d92f84a207548d

View on Chainz ↗

Height

#284,058

Difficulty

9.982070

Transactions

Size

1.59 KB

Version

Bits

09fb68f5

Nonce

20,058

Timestamp

11/29/2013, 11:55:07 PM

Confirmations

6,515,316

Mined by

⛏️ P2SHAbGkvdxHZ4BVXfnK4PvSdcrNAUoihMdBXd

Merkle Root

b4c270afcd36b8477f8b413765abbabd7336a5cbededb58c187adddbe6636208

Transactions (3)

Coinbasec990d020d64596…b2e99ecceba099

1 in → 1 out10.0400 XPM100 B

AbGkvdxH…oihMdBXd

6661eff2936d8e…abf728aca4b019

3 in → 8 out30.1000 XPM623 B

AWNBjSo4…YHqt9QnU AK3vz3dH…9NvorskL ARHdqAGQ…eRCHyCYQ AU6bVD2o…JjzwJGx9 AFx4pUv4…deee42SL

7e48a409c76673…c727702f9d933a

5 in → 2 out36.1166 XPM817 B

AavMJQCv…dfqwJkXM AYyWeDDa…msPT54Hu

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.

7.160 × 10⁹¹(92-digit number)

71604783410816154452…94851206503693330839

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

7.160 × 10⁹¹(92-digit number)

71604783410816154452…94851206503693330839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.160 × 10⁹¹(92-digit number)

71604783410816154452…94851206503693330841

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

1.432 × 10⁹²(93-digit number)

14320956682163230890…89702413007386661679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.432 × 10⁹²(93-digit number)

14320956682163230890…89702413007386661681

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

2.864 × 10⁹²(93-digit number)

28641913364326461780…79404826014773323359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.864 × 10⁹²(93-digit number)

28641913364326461780…79404826014773323361

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

5.728 × 10⁹²(93-digit number)

57283826728652923561…58809652029546646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.728 × 10⁹²(93-digit number)

57283826728652923561…58809652029546646721

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

1.145 × 10⁹³(94-digit number)

11456765345730584712…17619304059093293439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.145 × 10⁹³(94-digit number)

11456765345730584712…17619304059093293441

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