Block #169,843

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/18/2013, 7:50:56 AM · Difficulty 9.8669 · 6,647,239 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85ccc70172b41790d711e4465e2b37ffb00758505631f49cb959d9b2dffa8883

View on Chainz ↗

Height

#169,843

Difficulty

9.866890

Transactions

Size

356 B

Version

Bits

09ddec7a

Nonce

5,250

Timestamp

9/18/2013, 7:50:56 AM

Confirmations

6,647,239

Mined by

⛏️ P2SHAPDk6DTDPDT6JVpKF9USYKHLuchntSWZvH

Merkle Root

ca684cabd2a456318a0700002364917a453382be7bd0957f7d0049cee32b12ed

Transactions (2)

Coinbasebb1c6d4c79c819…eef567ea95bd55

1 in → 1 out10.2700 XPM109 B

APDk6DTD…hntSWZvH

f3acb85d519fd4…3e359a3df44c77

1 in → 1 out10.2500 XPM158 B

AN7CTbAY…CXZXPsEU

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.

1.701 × 10⁹²(93-digit number)

17018836005525330850…20445751160372066709

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

1.701 × 10⁹²(93-digit number)

17018836005525330850…20445751160372066709

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.701 × 10⁹²(93-digit number)

17018836005525330850…20445751160372066711

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

3.403 × 10⁹²(93-digit number)

34037672011050661701…40891502320744133419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.403 × 10⁹²(93-digit number)

34037672011050661701…40891502320744133421

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

6.807 × 10⁹²(93-digit number)

68075344022101323403…81783004641488266839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.807 × 10⁹²(93-digit number)

68075344022101323403…81783004641488266841

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

1.361 × 10⁹³(94-digit number)

13615068804420264680…63566009282976533679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.361 × 10⁹³(94-digit number)

13615068804420264680…63566009282976533681

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

2.723 × 10⁹³(94-digit number)

27230137608840529361…27132018565953067359

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 #169,843

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