Block #149,100

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 3:49:03 AM · Difficulty 9.8568 · 6,640,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb702d21c7cb2b4539e847a4fcf8bbacdd7936d21d57c5f385a3aa5712eed674

View on Chainz ↗

Height

#149,100

Difficulty

9.856765

Transactions

Size

197 B

Version

Bits

09db54ed

Nonce

628,439

Timestamp

9/4/2013, 3:49:03 AM

Confirmations

6,640,792

Merkle Root

8c499bf496ce9bebc2b61a83bea128177d25e0094f23c03a2d69f15853308994

Transactions (1)

Coinbase8c499bf496ce9b…69f15853308994

1 in → 1 out10.2800 XPM109 B

AbERMcut…QQKtkzeK

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.

3.745 × 10⁹⁰(91-digit number)

37453933527606565671…88687915058118422759

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

3.745 × 10⁹⁰(91-digit number)

37453933527606565671…88687915058118422759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.745 × 10⁹⁰(91-digit number)

37453933527606565671…88687915058118422761

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

7.490 × 10⁹⁰(91-digit number)

74907867055213131342…77375830116236845519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.490 × 10⁹⁰(91-digit number)

74907867055213131342…77375830116236845521

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

1.498 × 10⁹¹(92-digit number)

14981573411042626268…54751660232473691039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.498 × 10⁹¹(92-digit number)

14981573411042626268…54751660232473691041

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

2.996 × 10⁹¹(92-digit number)

29963146822085252536…09503320464947382079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.996 × 10⁹¹(92-digit number)

29963146822085252536…09503320464947382081

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

5.992 × 10⁹¹(92-digit number)

59926293644170505073…19006640929894764159

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