Block #284,855

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 6:59:58 AM · Difficulty 9.9834 · 6,548,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2473d3c6619fd034712a17ea6bb4f00dfcadf5f9f53ab6dc512427ea9bc40de9

View on Chainz ↗

Height

#284,855

Difficulty

9.983376

Transactions

Size

1.22 KB

Version

Bits

09fbbe8e

Nonce

137,065

Timestamp

11/30/2013, 6:59:58 AM

Confirmations

6,548,589

Mined by

⛏️ P2SHATTnCrw4WkmJCCr1Gbo4XVR3NnkAUSWcEs

Merkle Root

5e02eb666a4821443dc361a203ffa9a32e1f5970c2efa069efc0931bd2eba7c9

Transactions (5)

Coinbase6916395228d233…e86d6261451e3c

1 in → 1 out10.0700 XPM109 B

ATTnCrw4…kAUSWcEs

afb1042e3ffdb4…bfb8a57a02c072

1 in → 2 out7.9688 XPM226 B

AHe1PwkG…wU2VuEQM AYgx65aw…Xz3aXYUM

bafd0d60cbca19…bd5b83da1816a2

2 in → 2 out2.5321 XPM373 B

APdgCh7v…wVDXqCGz Ab3dSvM7…Qoxxb9tp

e72b47b73ac5e2…0fd5bb20ac6ccf

1 in → 2 out6.9091 XPM226 B

APBM67Tp…Xigg3wTX AVVxTgxU…fzsB7g8V

953f7dce4f4473…2d715b43329e6e

1 in → 2 out5.9547 XPM227 B

AWHqSsod…S114Gc1Y ATQU4Q12…ck5ZR9Wq

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.

2.197 × 10⁹⁴(95-digit number)

21976064924087856030…98418830032650649599

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

2.197 × 10⁹⁴(95-digit number)

21976064924087856030…98418830032650649599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.197 × 10⁹⁴(95-digit number)

21976064924087856030…98418830032650649601

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

4.395 × 10⁹⁴(95-digit number)

43952129848175712061…96837660065301299199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.395 × 10⁹⁴(95-digit number)

43952129848175712061…96837660065301299201

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

8.790 × 10⁹⁴(95-digit number)

87904259696351424122…93675320130602598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.790 × 10⁹⁴(95-digit number)

87904259696351424122…93675320130602598401

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

1.758 × 10⁹⁵(96-digit number)

17580851939270284824…87350640261205196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.758 × 10⁹⁵(96-digit number)

17580851939270284824…87350640261205196801

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

3.516 × 10⁹⁵(96-digit number)

35161703878540569648…74701280522410393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.516 × 10⁹⁵(96-digit number)

35161703878540569648…74701280522410393601

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 #284,855

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