Block #29,043

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 2:12:53 PM · Difficulty 7.9836 · 6,760,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a10728253558d25f544ffe7b173de0dc71f7579c3086526dd98c4afcdaeb31d

View on Chainz ↗

Height

#29,043

Difficulty

7.983615

Transactions

Size

1.38 KB

Version

Bits

07fbce2e

Nonce

493

Timestamp

7/13/2013, 2:12:53 PM

Confirmations

6,760,631

Merkle Root

34d84dcb41e0dc637b6b68cc92a4e79cd9292cd302a962d41bac1c85c75a725f

Transactions (2)

Coinbase37f9ccae9248b3…afea5ce48d4614

1 in → 1 out15.6900 XPM108 B

AK6GoqtS…oo9j9Qbm

1b4e167f9a5041…429dc53ee66b7f

10 in → 1 out148.4100 XPM1.19 KB

AKfeR8gS…LNjUzaey

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.

5.334 × 10⁹⁴(95-digit number)

53342480289984812327…99878433162114363649

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

5.334 × 10⁹⁴(95-digit number)

53342480289984812327…99878433162114363649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.334 × 10⁹⁴(95-digit number)

53342480289984812327…99878433162114363651

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

1.066 × 10⁹⁵(96-digit number)

10668496057996962465…99756866324228727299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.066 × 10⁹⁵(96-digit number)

10668496057996962465…99756866324228727301

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

2.133 × 10⁹⁵(96-digit number)

21336992115993924930…99513732648457454599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.133 × 10⁹⁵(96-digit number)

21336992115993924930…99513732648457454601

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

4.267 × 10⁹⁵(96-digit number)

42673984231987849861…99027465296914909199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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