Block #248,175

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 5:42:24 AM · Difficulty 9.9654 · 6,548,620 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b8a4f3c6f0c81caeee6a772198724862d73f16bf549024f858e16c62fdcf0ab

View on Chainz ↗

Height

#248,175

Difficulty

9.965425

Transactions

Size

1.25 KB

Version

Bits

09f7261c

Nonce

11,902

Timestamp

11/7/2013, 5:42:24 AM

Confirmations

6,548,620

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

b891cd3f843a3b75633d69382bdae5290342ff8f269a6a7aef2790f90ca8c156

Transactions (5)

Coinbase16a4dc7da783c8…d12a756b00e759

1 in → 2 out10.0900 XPM137 B

AZDUEbdS…RYKMRZET AU6kq4CL…dQBLvxLp

bf9c16367cd9d4…1eb9e7ab21601c

1 in → 2 out8.0384 XPM227 B

AMV2CWW7…yebsFBrS AMBmzEn9…nqsp7e1n

3e671d3b17f499…1b070e45edab75

1 in → 2 out5.0260 XPM226 B

Ac44Dow2…Mvwe36r8 AMJDChGB…VXxUjXFK

a5887d8217db48…5a87988c73443c

1 in → 2 out4.4045 XPM226 B

ATqDht7F…xHD53DYv Ac4vPc2j…h2YB1q1m

02e01ac4542a28…2d4732c973eab1

2 in → 2 out5.0204 XPM375 B

AN3QK9wE…SHQv3wVg AR874DKu…rHPPpaBG

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.

7.771 × 10⁹⁶(97-digit number)

77711027542479789979…37384784381686604799

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

7.771 × 10⁹⁶(97-digit number)

77711027542479789979…37384784381686604799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.771 × 10⁹⁶(97-digit number)

77711027542479789979…37384784381686604801

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

1.554 × 10⁹⁷(98-digit number)

15542205508495957995…74769568763373209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.554 × 10⁹⁷(98-digit number)

15542205508495957995…74769568763373209601

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

3.108 × 10⁹⁷(98-digit number)

31084411016991915991…49539137526746419199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.108 × 10⁹⁷(98-digit number)

31084411016991915991…49539137526746419201

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

6.216 × 10⁹⁷(98-digit number)

62168822033983831983…99078275053492838399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.216 × 10⁹⁷(98-digit number)

62168822033983831983…99078275053492838401

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

1.243 × 10⁹⁸(99-digit number)

12433764406796766396…98156550106985676799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.243 × 10⁹⁸(99-digit number)

12433764406796766396…98156550106985676801

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