Block #249,340

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 9:59:15 PM · Difficulty 9.9667 · 6,545,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5480b3f3a563fa607595aec5ee606cbb1d09419a48276e28ce44117214a2fa4

View on Chainz ↗

Height

#249,340

Difficulty

9.966735

Transactions

Size

428 B

Version

Bits

09f77bf0

Nonce

21,419

Timestamp

11/7/2013, 9:59:15 PM

Confirmations

6,545,244

Mined by

⛏️ P2SHAQaCJsaU5a69V8Dtjoc2inAzh8MRLEgb1G

Merkle Root

802dc340443f1531fcfac83c97b009bb255ac49c9caf8ff8c975671af610ec83

Transactions (2)

Coinbased1766dee5da39f…8a2bf8a92e0000

1 in → 1 out10.0600 XPM109 B

AQaCJsaU…MRLEgb1G

a91b9c99cf44fc…e18aa39860d182

1 in → 2 out87.9971 XPM227 B

AZdmkNt9…Dk8ffFeU AYKzi7qK…TT3HJZ1t

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.

1.653 × 10¹⁰⁰(101-digit number)

16531062243433517049…39197257537969395409

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

1.653 × 10¹⁰⁰(101-digit number)

16531062243433517049…39197257537969395409

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.653 × 10¹⁰⁰(101-digit number)

16531062243433517049…39197257537969395411

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

3.306 × 10¹⁰⁰(101-digit number)

33062124486867034098…78394515075938790819

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.306 × 10¹⁰⁰(101-digit number)

33062124486867034098…78394515075938790821

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

6.612 × 10¹⁰⁰(101-digit number)

66124248973734068197…56789030151877581639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.612 × 10¹⁰⁰(101-digit number)

66124248973734068197…56789030151877581641

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

1.322 × 10¹⁰¹(102-digit number)

13224849794746813639…13578060303755163279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.322 × 10¹⁰¹(102-digit number)

13224849794746813639…13578060303755163281

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

2.644 × 10¹⁰¹(102-digit number)

26449699589493627279…27156120607510326559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.644 × 10¹⁰¹(102-digit number)

26449699589493627279…27156120607510326561

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