Block #144,998

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 3:35:45 PM · Difficulty 9.8418 · 6,649,585 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74c215eebce780d543b0e577facf7f66b8aa249faf90daab6ac38b3fd5d5811b

View on Chainz ↗

Height

#144,998

Difficulty

9.841812

Transactions

Size

356 B

Version

Bits

09d78100

Nonce

5,550

Timestamp

9/1/2013, 3:35:45 PM

Confirmations

6,649,585

Mined by

⛏️ P2SHAKhaGKFX4s17sd56QzVFtsa8mSKjeAXtBv

Merkle Root

0098778acb02d155ad1b13eccfea1695ce4c50061307ac7c073da28fa33304c9

Transactions (2)

Coinbasea488a8d34079da…7fb768e5d784ac

1 in → 1 out10.3200 XPM109 B

AKhaGKFX…KjeAXtBv

5df56f3602ed8a…f82c412dbaf43a

1 in → 1 out10.3100 XPM157 B

AREtHCxv…ibjFLuz3

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.

6.137 × 10⁹⁴(95-digit number)

61379291891492597780…60619655578201193579

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

6.137 × 10⁹⁴(95-digit number)

61379291891492597780…60619655578201193579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.137 × 10⁹⁴(95-digit number)

61379291891492597780…60619655578201193581

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

1.227 × 10⁹⁵(96-digit number)

12275858378298519556…21239311156402387159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.227 × 10⁹⁵(96-digit number)

12275858378298519556…21239311156402387161

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

2.455 × 10⁹⁵(96-digit number)

24551716756597039112…42478622312804774319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.455 × 10⁹⁵(96-digit number)

24551716756597039112…42478622312804774321

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

4.910 × 10⁹⁵(96-digit number)

49103433513194078224…84957244625609548639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.910 × 10⁹⁵(96-digit number)

49103433513194078224…84957244625609548641

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

9.820 × 10⁹⁵(96-digit number)

98206867026388156448…69914489251219097279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.820 × 10⁹⁵(96-digit number)

98206867026388156448…69914489251219097281

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