Block #170,143

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/18/2013, 1:31:30 PM · Difficulty 9.8659 · 6,645,871 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c076f794a797ede53b541e570326d2b161d33d4cbfb3d24e0e75252cd744a7e6

View on Chainz ↗

Height

#170,143

Difficulty

9.865851

Transactions

Size

686 B

Version

Bits

09dda863

Nonce

631

Timestamp

9/18/2013, 1:31:30 PM

Confirmations

6,645,871

Mined by

⛏️ P2SHAe6PYBDNs6MFPfqSfG8TyUUBAHjSQhB18y

Merkle Root

83f0418211001ba046a2ab635951c2e550f8aeb616a83ce17cd6c8f504ee2641

Transactions (2)

Coinbase05ab1d86ced7a0…985b5149058c4a

1 in → 1 out10.2713 XPM109 B

Ae6PYBDN…jSQhB18y

83f66271fd615e…c178191b60eb26

3 in → 1 out2041.9900 XPM488 B

ANiZHutm…8LERTY5V

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.

2.239 × 10⁹¹(92-digit number)

22399142199836152183…88660808003091323199

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

2.239 × 10⁹¹(92-digit number)

22399142199836152183…88660808003091323199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.239 × 10⁹¹(92-digit number)

22399142199836152183…88660808003091323201

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

4.479 × 10⁹¹(92-digit number)

44798284399672304367…77321616006182646399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.479 × 10⁹¹(92-digit number)

44798284399672304367…77321616006182646401

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

8.959 × 10⁹¹(92-digit number)

89596568799344608735…54643232012365292799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.959 × 10⁹¹(92-digit number)

89596568799344608735…54643232012365292801

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

1.791 × 10⁹²(93-digit number)

17919313759868921747…09286464024730585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.791 × 10⁹²(93-digit number)

17919313759868921747…09286464024730585601

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

3.583 × 10⁹²(93-digit number)

35838627519737843494…18572928049461171199

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 #170,143

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