Block #248,523

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 10:46:37 AM · Difficulty 9.9657 · 6,543,601 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf28a30efee636186597cb740c94c5a5bbb225e953c1218d637a5986642496fc

View on Chainz ↗

Height

#248,523

Difficulty

9.965741

Transactions

Size

452 B

Version

Bits

09f73ac8

Nonce

3,797

Timestamp

11/7/2013, 10:46:37 AM

Confirmations

6,543,601

Merkle Root

7a9a86676c71c41b9885ebc66bcd095bbac2ca543661ae64817583abeed061ca

Transactions (2)

Coinbasef0cfc7fb1503ef…b69203f3084174

1 in → 2 out10.0600 XPM136 B

AZDUEbdS…RYKMRZET ASNt3cJa…L5zCqAYM

6fa9d22b872880…dcb55209659d42

1 in → 2 out6.0263 XPM226 B

Ad7Prw5J…DK4AQxpE AMW1R2xY…HnG2vF3J

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.

1.198 × 10⁹⁵(96-digit number)

11980787534998912054…63966247916345151539

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

1.198 × 10⁹⁵(96-digit number)

11980787534998912054…63966247916345151539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.198 × 10⁹⁵(96-digit number)

11980787534998912054…63966247916345151541

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

2.396 × 10⁹⁵(96-digit number)

23961575069997824108…27932495832690303079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.396 × 10⁹⁵(96-digit number)

23961575069997824108…27932495832690303081

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

4.792 × 10⁹⁵(96-digit number)

47923150139995648216…55864991665380606159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.792 × 10⁹⁵(96-digit number)

47923150139995648216…55864991665380606161

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

9.584 × 10⁹⁵(96-digit number)

95846300279991296432…11729983330761212319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.584 × 10⁹⁵(96-digit number)

95846300279991296432…11729983330761212321

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

1.916 × 10⁹⁶(97-digit number)

19169260055998259286…23459966661522424639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.916 × 10⁹⁶(97-digit number)

19169260055998259286…23459966661522424641

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