Block #178,187

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/24/2013, 5:31:49 AM · Difficulty 9.8633 · 6,617,094 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cdfc4a0d1bef48d556f266cb8c3a6b1cfe5579f50e396c789cb0fa9bfbed14db

View on Chainz ↗

Height

#178,187

Difficulty

9.863252

Transactions

Size

1.45 KB

Version

Bits

09dcfe11

Nonce

8,077

Timestamp

9/24/2013, 5:31:49 AM

Confirmations

6,617,094

Mined by

⛏️ P2SHAQtKa2VGCfjh7ujSJop8otQwJezrkSdNFZ

Merkle Root

6db8eb845f4d6dff0974dfc016f5223c9d71d5841b8ce6935c18d81b90947e6c

Transactions (3)

Coinbase2abe2d67348a8e…ca4c03b3eedbe5

1 in → 1 out10.2800 XPM109 B

AQtKa2VG…zrkSdNFZ

fec9943e2bad07…b013d7b6e4c95e

6 in → 2 out61.7000 XPM763 B

AZiZ3BSK…ouABkYiL AMaGS72Y…FoQLssKL

e7759259edeef2…c1012f5e849dc1

3 in → 2 out10.0163 XPM519 B

AaVATm2K…Woofrhiq AaFegKWR…UCo6GwpD

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.

1.048 × 10⁹⁴(95-digit number)

10484359141052984841…84059211305831399999

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

1.048 × 10⁹⁴(95-digit number)

10484359141052984841…84059211305831399999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.048 × 10⁹⁴(95-digit number)

10484359141052984841…84059211305831400001

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

2.096 × 10⁹⁴(95-digit number)

20968718282105969682…68118422611662799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.096 × 10⁹⁴(95-digit number)

20968718282105969682…68118422611662800001

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

4.193 × 10⁹⁴(95-digit number)

41937436564211939364…36236845223325599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.193 × 10⁹⁴(95-digit number)

41937436564211939364…36236845223325600001

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

8.387 × 10⁹⁴(95-digit number)

83874873128423878729…72473690446651199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.387 × 10⁹⁴(95-digit number)

83874873128423878729…72473690446651200001

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

1.677 × 10⁹⁵(96-digit number)

16774974625684775745…44947380893302399999

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