Block #106,937

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/9/2013, 6:32:07 AM · Difficulty 9.6187 · 6,698,741 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f77277365602a00fee5f099cf8f22973fa9c3698f8a92a7f95245631ce90aeba

View on Chainz ↗

Height

#106,937

Difficulty

9.618656

Transactions

Size

4.44 KB

Version

Bits

099e6045

Nonce

Timestamp

8/9/2013, 6:32:07 AM

Confirmations

6,698,741

Mined by

⛏️ P2SHAUUxbJqKggn1MQiMCBuv4FXcxBNAWzLxaM

Merkle Root

0d7bd94e7a3854fed408072ddacb42ad69939911bbb364d527660fa4c941bf7a

Transactions (3)

Coinbasee61600c7c54331…28b5b2f8a0ecfe

1 in → 1 out10.8500 XPM110 B

AUUxbJqK…NAWzLxaM

a1930b602a3093…8c4524d7788d7d

1 in → 1 out11.1500 XPM159 B

ASiFSskY…tnHV7M4n

40da036579cb7b…9a9895e599ace8

36 in → 2 out396.8100 XPM4.08 KB

ALMKdpef…ehXinMdh AdNeXXkk…QpfXAns4

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.

4.469 × 10¹⁰³(104-digit number)

44697756765021117220…99058319880665806219

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

4.469 × 10¹⁰³(104-digit number)

44697756765021117220…99058319880665806219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.469 × 10¹⁰³(104-digit number)

44697756765021117220…99058319880665806221

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

8.939 × 10¹⁰³(104-digit number)

89395513530042234440…98116639761331612439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.939 × 10¹⁰³(104-digit number)

89395513530042234440…98116639761331612441

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

1.787 × 10¹⁰⁴(105-digit number)

17879102706008446888…96233279522663224879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.787 × 10¹⁰⁴(105-digit number)

17879102706008446888…96233279522663224881

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

3.575 × 10¹⁰⁴(105-digit number)

35758205412016893776…92466559045326449759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.575 × 10¹⁰⁴(105-digit number)

35758205412016893776…92466559045326449761

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

7.151 × 10¹⁰⁴(105-digit number)

71516410824033787552…84933118090652899519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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