Block #175,272

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 4:34:01 AM · Difficulty 9.8637 · 6,621,629 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd382f0443302f90ffbd9cf9d10c7921c4ebe5098a9600d567902bd80902f567

View on Chainz ↗

Height

#175,272

Difficulty

9.863727

Transactions

Size

1.58 KB

Version

Bits

09dd1d39

Nonce

11,742

Timestamp

9/22/2013, 4:34:01 AM

Confirmations

6,621,629

Mined by

⛏️ P2SHAcprKFHC4Fvm4QCAFyZqCh4ovAD4cVWMLN

Merkle Root

154d6716bd38f088335030b84e96fede1064af56ecaa091887c8652c258f03ad

Transactions (4)

Coinbase9a1984a7614c6c…3bf5d36d23d8c3

1 in → 1 out10.2900 XPM109 B

AcprKFHC…D4cVWMLN

665227f9f69902…1ec5c6d669d4b0

6 in → 2 out40.3135 XPM965 B

Adr2MdAr…YAm7L5kq AZbnPqqW…8cDz5Rfd

92a144acad209d…95b5ae5806a595

1 in → 2 out5.8473 XPM225 B

AGnaKoh5…eKUvRrPQ AaQZaxip…Sg1zsYBg

1357f402635a29…b5a37c4795da05

1 in → 2 out2.1428 XPM227 B

AedCcZFg…4Je2si2d AQFBW6Ev…RQ4H4EFe

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.

7.132 × 10⁹⁸(99-digit number)

71325190690704948174…69424738426055695999

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

7.132 × 10⁹⁸(99-digit number)

71325190690704948174…69424738426055695999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.132 × 10⁹⁸(99-digit number)

71325190690704948174…69424738426055696001

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

1.426 × 10⁹⁹(100-digit number)

14265038138140989634…38849476852111391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.426 × 10⁹⁹(100-digit number)

14265038138140989634…38849476852111392001

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

2.853 × 10⁹⁹(100-digit number)

28530076276281979269…77698953704222783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.853 × 10⁹⁹(100-digit number)

28530076276281979269…77698953704222784001

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

5.706 × 10⁹⁹(100-digit number)

57060152552563958539…55397907408445567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.706 × 10⁹⁹(100-digit number)

57060152552563958539…55397907408445568001

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

1.141 × 10¹⁰⁰(101-digit number)

11412030510512791707…10795814816891135999

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