Block #183,950

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 8:43:28 AM · Difficulty 9.8586 · 6,622,228 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3532f64c4795ad9b8ca634f130a9bfefa87c35691226bd8e8d65c863aee097e2

View on Chainz ↗

Height

#183,950

Difficulty

9.858584

Transactions

Size

722 B

Version

Bits

09dbcc27

Nonce

33,340

Timestamp

9/28/2013, 8:43:28 AM

Confirmations

6,622,228

Mined by

⛏️ P2SHANGtmL1gj9zEyTai83MwpvE1pvs5c9mevS

Merkle Root

4ff2c547eb0a3c247fd2d910a2b8b6796a0a8da77e094b196fd049940a2f68d9

Transactions (2)

Coinbase968fd81b0da288…483c64a5a767f0

1 in → 1 out10.2800 XPM109 B

ANGtmL1g…s5c9mevS

5ccfb3bc9a2a4f…6e8afffe982cad

3 in → 2 out400.0103 XPM522 B

ASDVBfFZ…JizKJugo AZWMamXP…j5gnXzvx

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.

6.134 × 10⁹⁶(97-digit number)

61345151690725417637…74331297017315651199

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

6.134 × 10⁹⁶(97-digit number)

61345151690725417637…74331297017315651199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.134 × 10⁹⁶(97-digit number)

61345151690725417637…74331297017315651201

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

1.226 × 10⁹⁷(98-digit number)

12269030338145083527…48662594034631302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.226 × 10⁹⁷(98-digit number)

12269030338145083527…48662594034631302401

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

2.453 × 10⁹⁷(98-digit number)

24538060676290167054…97325188069262604799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.453 × 10⁹⁷(98-digit number)

24538060676290167054…97325188069262604801

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

4.907 × 10⁹⁷(98-digit number)

49076121352580334109…94650376138525209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.907 × 10⁹⁷(98-digit number)

49076121352580334109…94650376138525209601

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

9.815 × 10⁹⁷(98-digit number)

98152242705160668219…89300752277050419199

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