Block #275,388

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 4:36:24 PM · Difficulty 9.9606 · 6,519,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a80097fe219aae5afcff07b9eaf6b1284414545c0aa7b1f29b9f4fd3584f4f11

View on Chainz ↗

Height

#275,388

Difficulty

9.960621

Transactions

Size

2.58 KB

Version

Bits

09f5eb3e

Nonce

6,333

Timestamp

11/26/2013, 4:36:24 PM

Confirmations

6,519,487

Mined by

⛏️ P2SHAVExKqaghUbBZia7FxgBmuzi8Q3aF9R3FX

Merkle Root

f7df78b8b772cc98c534fabe5b529beb1eadbfa1b99a2a4d97f2f0fdd63e7a3c

Transactions (2)

Coinbase8205545b4077a3…c6aa678b9908dc

1 in → 1 out10.0900 XPM109 B

AVExKqag…3aF9R3FX

474f404e3ddb84…daf81ccd8dece9

16 in → 2 out132.6866 XPM2.39 KB

AcVpEMuW…2Lt4MNUE AetaiqbQ…4vZf9SwK

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.

3.976 × 10⁹¹(92-digit number)

39764373166748634540…78304830849541584399

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

3.976 × 10⁹¹(92-digit number)

39764373166748634540…78304830849541584399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.976 × 10⁹¹(92-digit number)

39764373166748634540…78304830849541584401

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

7.952 × 10⁹¹(92-digit number)

79528746333497269081…56609661699083168799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.952 × 10⁹¹(92-digit number)

79528746333497269081…56609661699083168801

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

1.590 × 10⁹²(93-digit number)

15905749266699453816…13219323398166337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.590 × 10⁹²(93-digit number)

15905749266699453816…13219323398166337601

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

3.181 × 10⁹²(93-digit number)

31811498533398907632…26438646796332675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.181 × 10⁹²(93-digit number)

31811498533398907632…26438646796332675201

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

6.362 × 10⁹²(93-digit number)

63622997066797815264…52877293592665350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.362 × 10⁹²(93-digit number)

63622997066797815264…52877293592665350401

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