Block #173,092

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/20/2013, 5:41:18 PM · Difficulty 9.8612 · 6,622,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce4b391fc0fcedfc0cef4bb7f9144804281f715a3a0fa377e4402a926f9ca477

View on Chainz ↗

Height

#173,092

Difficulty

9.861190

Transactions

Size

1.31 KB

Version

Bits

09dc76f1

Nonce

3,118

Timestamp

9/20/2013, 5:41:18 PM

Confirmations

6,622,747

Mined by

⛏️ P2SHAHjPH1SJZB2F3fbzEG1ruNeLC5pZgkdLmi

Merkle Root

0621709aaf266c138fb4580c614e86107de72e8040841dcedc04c9ab22368a0f

Transactions (3)

Coinbasea5ed0e54aca26d…7691cee88a23a7

1 in → 1 out10.2900 XPM109 B

AHjPH1SJ…pZgkdLmi

f00b69c4279b59…969233f64e4313

4 in → 6 out15.7884 XPM772 B

Ac5sZcdP…kzV4eckG APG1sURm…38ZvSiMo AM7V4EEN…eyp6TL3r AWP3nWpc…wKY1EyHx ALVaS9Pa…WUbnL1Gt

e8519b5786a246…98188a4c4d59f8

2 in → 2 out2.0886 XPM372 B

AQFBW6Ev…RQ4H4EFe AHePWBYf…nPnh5two

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.

8.603 × 10⁹³(94-digit number)

86035192790693781741…49917266380079948799

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

8.603 × 10⁹³(94-digit number)

86035192790693781741…49917266380079948799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.603 × 10⁹³(94-digit number)

86035192790693781741…49917266380079948801

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

1.720 × 10⁹⁴(95-digit number)

17207038558138756348…99834532760159897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.720 × 10⁹⁴(95-digit number)

17207038558138756348…99834532760159897601

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

3.441 × 10⁹⁴(95-digit number)

34414077116277512696…99669065520319795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.441 × 10⁹⁴(95-digit number)

34414077116277512696…99669065520319795201

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

6.882 × 10⁹⁴(95-digit number)

68828154232555025393…99338131040639590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.882 × 10⁹⁴(95-digit number)

68828154232555025393…99338131040639590401

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

1.376 × 10⁹⁵(96-digit number)

13765630846511005078…98676262081279180799

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