Block #248,119

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 4:50:42 AM · Difficulty 9.9654 · 6,550,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5ccc13764920ee3f3b2d541c49a619fc9fbc12479e07ffc42110591734c5a615

View on Chainz ↗

Height

#248,119

Difficulty

9.965396

Transactions

Size

605 B

Version

Bits

09f7242b

Nonce

9,720

Timestamp

11/7/2013, 4:50:42 AM

Confirmations

6,550,673

Mined by

⛏️ P2SHAeL7UAFbYJxtsFPY1Wp7S8F2EUW9mPDyGL

Merkle Root

235537ddee1bf41052bcfd5e510c467dba102ba98eb92027c900b440fd3bb398

Transactions (2)

Coinbase202e6c41b6efa2…a102b64e0fa61c

1 in → 2 out10.0600 XPM137 B

AeL7UAFb…W9mPDyGL AHsw4d6U…EnM8UXNZ

20bca3dbec5cb3…a21ee2a2a3a3df

2 in → 2 out254.3525 XPM375 B

AcKLM1HS…a2si63Un AaiFSpvX…n3SS7r8o

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.

1.323 × 10¹⁰¹(102-digit number)

13234922733790376097…58094993649625695999

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

1.323 × 10¹⁰¹(102-digit number)

13234922733790376097…58094993649625695999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.323 × 10¹⁰¹(102-digit number)

13234922733790376097…58094993649625696001

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

2.646 × 10¹⁰¹(102-digit number)

26469845467580752194…16189987299251391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.646 × 10¹⁰¹(102-digit number)

26469845467580752194…16189987299251392001

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

5.293 × 10¹⁰¹(102-digit number)

52939690935161504389…32379974598502783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.293 × 10¹⁰¹(102-digit number)

52939690935161504389…32379974598502784001

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

1.058 × 10¹⁰²(103-digit number)

10587938187032300877…64759949197005567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.058 × 10¹⁰²(103-digit number)

10587938187032300877…64759949197005568001

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

2.117 × 10¹⁰²(103-digit number)

21175876374064601755…29519898394011135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.117 × 10¹⁰²(103-digit number)

21175876374064601755…29519898394011136001

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