Block #276,259

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/27/2013, 2:30:11 AM · Difficulty 9.9628 · 6,523,317 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43d86155d87138e5c8441ef1e82d859a566aab08659a4303e971de7ca44e75cc

View on Chainz ↗

Height

#276,259

Difficulty

9.962760

Transactions

Size

1.51 KB

Version

Bits

09f67773

Nonce

105,457

Timestamp

11/27/2013, 2:30:11 AM

Confirmations

6,523,317

Mined by

⛏️ #7aRYAWA5FEzr1qnwaQdA5YUZ1J3dasx9RdPKTy

Merkle Root

f5b4e117bcf1543c9d47b82002685a3c397fa0acbc54e8e56535b8733d988a58

Transactions (2)

Coinbaseaf45951bbcbd4b…e26f259831a669

1 in → 30 out10.0400 XPM1.06 KB

AWA5FEzr…x9RdPKTy AVss9H5F…zXhyMijY AR8VbaR5…dZqkQer1 AY6MvLfB…Z3ZLcoYn AQBqYP46…NcWpkngb

d0e1c5b4a72dfd…ccf0e5418b3f82

2 in → 2 out5.0582 XPM374 B

AexHmbhk…6aXorNBq AJYvM6wF…256DsSqJ

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.

1.203 × 10⁹²(93-digit number)

12035145801934499553…11723164422197999999

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

1.203 × 10⁹²(93-digit number)

12035145801934499553…11723164422197999999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.203 × 10⁹²(93-digit number)

12035145801934499553…11723164422198000001

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

2.407 × 10⁹²(93-digit number)

24070291603868999106…23446328844395999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.407 × 10⁹²(93-digit number)

24070291603868999106…23446328844396000001

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

4.814 × 10⁹²(93-digit number)

48140583207737998212…46892657688791999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.814 × 10⁹²(93-digit number)

48140583207737998212…46892657688792000001

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

9.628 × 10⁹²(93-digit number)

96281166415475996424…93785315377583999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.628 × 10⁹²(93-digit number)

96281166415475996424…93785315377584000001

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

1.925 × 10⁹³(94-digit number)

19256233283095199284…87570630755167999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.925 × 10⁹³(94-digit number)

19256233283095199284…87570630755168000001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.851 × 10⁹³(94-digit number)

38512466566190398569…75141261510335999999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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