Block #289,998

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 11:40:38 AM · Difficulty 9.9889 · 6,504,732 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c3d7e5826886707301f22aef969917fd55e5c2d34faba9e9e98b46d5e5f99698

View on Chainz ↗

Height

#289,998

Difficulty

9.988921

Transactions

Size

1021 B

Version

Bits

09fd29f3

Nonce

517,045

Timestamp

12/2/2013, 11:40:38 AM

Confirmations

6,504,732

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

108aac06e7409b6865a97b1343c0e7a219dfd78339d940005460ee0f84049e52

Transactions (2)

Coinbaseaedbe2dcd7d669…fab1324f5a6d64

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

97d0d640e085cb…edab0ae19af7f8

5 in → 2 out2.2235 XPM820 B

AenDvzQB…bGyej5Nd AdygwDHr…hCUyB95K

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.

3.176 × 10⁹⁷(98-digit number)

31769848438398333713…85402390994529034239

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

3.176 × 10⁹⁷(98-digit number)

31769848438398333713…85402390994529034239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.176 × 10⁹⁷(98-digit number)

31769848438398333713…85402390994529034241

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

6.353 × 10⁹⁷(98-digit number)

63539696876796667426…70804781989058068479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.353 × 10⁹⁷(98-digit number)

63539696876796667426…70804781989058068481

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

1.270 × 10⁹⁸(99-digit number)

12707939375359333485…41609563978116136959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.270 × 10⁹⁸(99-digit number)

12707939375359333485…41609563978116136961

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

2.541 × 10⁹⁸(99-digit number)

25415878750718666970…83219127956232273919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.541 × 10⁹⁸(99-digit number)

25415878750718666970…83219127956232273921

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

5.083 × 10⁹⁸(99-digit number)

50831757501437333941…66438255912464547839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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