Block #186,668

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/30/2013, 1:11:29 AM · Difficulty 9.8670 · 6,630,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

680c9da91972707756735df9f78300c1a8ee2825b81c71b3a300fc8b90e13904

View on Chainz ↗

Height

#186,668

Difficulty

9.866985

Transactions

Size

2.30 KB

Version

Bits

09ddf2b5

Nonce

44,262

Timestamp

9/30/2013, 1:11:29 AM

Confirmations

6,630,602

Mined by

⛏️ P2SHARqB87W6LvvLEGGxdFZLn67cbfnk1mj1h5

Merkle Root

c9c52b36220d3fee1f3f45cb7027e2ade3d8ae45da6c24756a288482bf59af35

Transactions (4)

Coinbasea0da9f6ee1a95b…94db5326fd4f7a

1 in → 1 out10.5800 XPM109 B

ARqB87W6…nk1mj1h5

5655ec031baf1d…0be7fa3597f5cf

10 in → 2 out134.8244 XPM1.52 KB

AJYtHvvV…6b9gzy7s AJiXWkay…Xf9pPTAq

7dd918e0cc2e90…25a19e492c5568

2 in → 2 out18.5000 XPM374 B

ALpthvGg…D1g5z4CT AaML3PX1…3qA2XBd1

c557202aaebba2…7a8b4a42a04970

1 in → 2 out8.2455 XPM227 B

AU87Aa1S…cq6QCRTQ ANm5tiLe…G92mwZF4

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.

2.883 × 10⁹⁴(95-digit number)

28831150726917193948…62247800169944299199

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

2.883 × 10⁹⁴(95-digit number)

28831150726917193948…62247800169944299199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.883 × 10⁹⁴(95-digit number)

28831150726917193948…62247800169944299201

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

5.766 × 10⁹⁴(95-digit number)

57662301453834387896…24495600339888598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.766 × 10⁹⁴(95-digit number)

57662301453834387896…24495600339888598401

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

1.153 × 10⁹⁵(96-digit number)

11532460290766877579…48991200679777196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.153 × 10⁹⁵(96-digit number)

11532460290766877579…48991200679777196801

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

2.306 × 10⁹⁵(96-digit number)

23064920581533755158…97982401359554393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.306 × 10⁹⁵(96-digit number)

23064920581533755158…97982401359554393601

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

4.612 × 10⁹⁵(96-digit number)

46129841163067510317…95964802719108787199

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 #186,668

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