Block #171,149

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/19/2013, 7:02:55 AM · Difficulty 9.8648 · 6,638,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32febe559ee0c3a99c0d56dc5cdf2c0b3b516ef046a56f1f91e80b2fd5c12e84

View on Chainz ↗

Height

#171,149

Difficulty

9.864777

Transactions

Size

3.90 KB

Version

Bits

09dd6205

Nonce

55,560

Timestamp

9/19/2013, 7:02:55 AM

Confirmations

6,638,660

Mined by

⛏️ P2SHAZvQk7wBCi3DVsQmZLTLQ8UkBm7Jt1zMKq

Merkle Root

ab09c425e1b1714d4ec9e4a196a38bb2c9a09f1a24b78643c61a2110ed51df9a

Transactions (4)

Coinbase5ad57b3f66948e…506c075de34082

1 in → 1 out10.3100 XPM109 B

AZvQk7wB…7Jt1zMKq

fed377d433ca2c…e50f432729a1e7

24 in → 2 out246.4500 XPM2.78 KB

AbJsT1MF…pF3oUXHW AaZTHvEh…QXHS2iBB

f5802c11b0a7e1…3fc394098739fe

5 in → 2 out38.5460 XPM714 B

ARyYtqtL…uCP66s1P APR9687B…mrcobDLy

3723a28c13f35b…b9dd351c5367bd

1 in → 2 out6.1834 XPM227 B

AaMmWiJ9…dSFc1UKk AHqyaJ8K…ZgjhBV3H

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.

3.421 × 10⁹⁵(96-digit number)

34215382294673183286…55038405145666585599

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

3.421 × 10⁹⁵(96-digit number)

34215382294673183286…55038405145666585599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.421 × 10⁹⁵(96-digit number)

34215382294673183286…55038405145666585601

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

6.843 × 10⁹⁵(96-digit number)

68430764589346366572…10076810291333171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.843 × 10⁹⁵(96-digit number)

68430764589346366572…10076810291333171201

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

1.368 × 10⁹⁶(97-digit number)

13686152917869273314…20153620582666342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.368 × 10⁹⁶(97-digit number)

13686152917869273314…20153620582666342401

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

2.737 × 10⁹⁶(97-digit number)

27372305835738546629…40307241165332684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.737 × 10⁹⁶(97-digit number)

27372305835738546629…40307241165332684801

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

5.474 × 10⁹⁶(97-digit number)

54744611671477093258…80614482330665369599

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

Block #171,149

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