Block #173,424

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/20/2013, 11:29:47 PM · Difficulty 9.8608 · 6,622,672 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8769f6093b98f13c21a64c3cd46fa1d238151ef9495cfb60b1f2650b4d1aa7bb

View on Chainz ↗

Height

#173,424

Difficulty

9.860792

Transactions

Size

1.16 KB

Version

Bits

09dc5cd8

Nonce

26,897

Timestamp

9/20/2013, 11:29:47 PM

Confirmations

6,622,672

Mined by

⛏️ P2SHAYrxrmY6ByfnQbGt47NFLJJGG63d5vcW8e

Merkle Root

82bdc88b6fa66f038c77ec0e3014f7620ac4a1191d7fc04572b1de08a031365f

Transactions (4)

Coinbase0d7528586b64d1…9ba954fc6d348e

1 in → 1 out10.3000 XPM109 B

AYrxrmY6…3d5vcW8e

4f18ca48b840ce…e2a4091a12110c

4 in → 2 out41.0700 XPM535 B

ARyYtqtL…uCP66s1P AKonrLQX…frQxbEB8

7e3fe1caf90915…f9b230186e325e

1 in → 2 out10.2400 XPM226 B

AcMbyaWm…1t3yeg9R AYjYQa47…bTfwhneM

c10414884c77c3…6fd7c95f028532

1 in → 2 out5.2299 XPM225 B

ANjE4rRU…gZ9FpSTJ AdET8Gt5…fBM7Hra6

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.

3.570 × 10⁹⁵(96-digit number)

35708403179221273979…65165057625619028479

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

3.570 × 10⁹⁵(96-digit number)

35708403179221273979…65165057625619028479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.570 × 10⁹⁵(96-digit number)

35708403179221273979…65165057625619028481

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

7.141 × 10⁹⁵(96-digit number)

71416806358442547959…30330115251238056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.141 × 10⁹⁵(96-digit number)

71416806358442547959…30330115251238056961

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

1.428 × 10⁹⁶(97-digit number)

14283361271688509591…60660230502476113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.428 × 10⁹⁶(97-digit number)

14283361271688509591…60660230502476113921

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

2.856 × 10⁹⁶(97-digit number)

28566722543377019183…21320461004952227839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.856 × 10⁹⁶(97-digit number)

28566722543377019183…21320461004952227841

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

5.713 × 10⁹⁶(97-digit number)

57133445086754038367…42640922009904455679

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