Block #146,606

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 2:55:02 PM · Difficulty 9.8483 · 6,651,205 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69c1dfcb339e53eb8d469ed78eae0e58c8428649ae118732d2c8b4a62e9376e5

View on Chainz ↗

Height

#146,606

Difficulty

9.848299

Transactions

Size

1.07 KB

Version

Bits

09d92a20

Nonce

70,373

Timestamp

9/2/2013, 2:55:02 PM

Confirmations

6,651,205

Mined by

⛏️ P2SHAKiWEmxn69vSqrvzHkZ84zwc6ZvgCgj6pm

Merkle Root

25abcfe749a46a8e2dc1e86c197acf996560633bcf4666c7faf5bc1f52b7cd3e

Transactions (3)

Coinbase7c4cb3fbcbced4…3676b7db315a24

1 in → 1 out10.3200 XPM109 B

AKiWEmxn…vgCgj6pm

a55b385fdc51f2…5369fe7451353d

2 in → 2 out48.5937 XPM373 B

ATrS65xS…guK8miLN AWFi3uMu…G9T6YpsE

ed331bcb1c11ff…ac5bc935553ee5

3 in → 2 out10.5187 XPM521 B

AHnvJDiF…j8QVpNpY Aba95JJe…uHsD9axX

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.

2.051 × 10⁹⁶(97-digit number)

20512750008724857784…14457328513932240639

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

2.051 × 10⁹⁶(97-digit number)

20512750008724857784…14457328513932240639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.051 × 10⁹⁶(97-digit number)

20512750008724857784…14457328513932240641

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

4.102 × 10⁹⁶(97-digit number)

41025500017449715569…28914657027864481279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.102 × 10⁹⁶(97-digit number)

41025500017449715569…28914657027864481281

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

8.205 × 10⁹⁶(97-digit number)

82051000034899431139…57829314055728962559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.205 × 10⁹⁶(97-digit number)

82051000034899431139…57829314055728962561

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

1.641 × 10⁹⁷(98-digit number)

16410200006979886227…15658628111457925119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.641 × 10⁹⁷(98-digit number)

16410200006979886227…15658628111457925121

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

3.282 × 10⁹⁷(98-digit number)

32820400013959772455…31317256222915850239

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