Block #106,636

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/9/2013, 3:15:55 AM · Difficulty 9.6107 · 6,696,786 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f4df66b70d44944cb3845e825f64519d4fccca0ae6cd5f6414c579298bc7859

View on Chainz ↗

Height

#106,636

Difficulty

9.610678

Transactions

Size

360 B

Version

Bits

099c556b

Nonce

144,037

Timestamp

8/9/2013, 3:15:55 AM

Confirmations

6,696,786

Mined by

⛏️ P2SHAJ7PsUMntjK4tUoxxrd92Ma9rqF6mf9Njr

Merkle Root

ba4db7a1dcf9c349489bef9aeba78e407d385f7cf6e2a77601475dc3a5f19ced

Transactions (2)

Coinbasef825b7ff110605…88041910296657

1 in → 1 out10.8200 XPM109 B

AJ7PsUMn…F6mf9Njr

6aff4b237ec203…c13c6e06640311

1 in → 1 out11.0100 XPM158 B

AZiCNyEn…BjhGoBch

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.

4.341 × 10¹⁰¹(102-digit number)

43415104839942779047…29303875937166146079

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

4.341 × 10¹⁰¹(102-digit number)

43415104839942779047…29303875937166146079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.341 × 10¹⁰¹(102-digit number)

43415104839942779047…29303875937166146081

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

8.683 × 10¹⁰¹(102-digit number)

86830209679885558094…58607751874332292159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.683 × 10¹⁰¹(102-digit number)

86830209679885558094…58607751874332292161

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

1.736 × 10¹⁰²(103-digit number)

17366041935977111618…17215503748664584319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.736 × 10¹⁰²(103-digit number)

17366041935977111618…17215503748664584321

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

3.473 × 10¹⁰²(103-digit number)

34732083871954223237…34431007497329168639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.473 × 10¹⁰²(103-digit number)

34732083871954223237…34431007497329168641

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

6.946 × 10¹⁰²(103-digit number)

69464167743908446475…68862014994658337279

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