Block #179,476

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/25/2013, 3:03:57 AM · Difficulty 9.8633 · 6,625,459 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f67377dd75ef5b906c06c2095de4583585b02a16bf3b190e47e296c3b2aa2527

View on Chainz ↗

Height

#179,476

Difficulty

9.863277

Transactions

Size

526 B

Version

Bits

09dcffc0

Nonce

1,164,776,238

Timestamp

9/25/2013, 3:03:57 AM

Confirmations

6,625,459

Mined by

⛏️ RBRAV4rziFj7Cxd8XM5wH4Y1cst3cQhTLsLyZ

Merkle Root

cb00f23edf66cb4c6a95d685ddc95e59229e5127a312dc8c4fb2142281470959

Transactions (1)

Coinbasecb00f23edf66cb…b2142281470959

1 in → 11 out10.2600 XPM436 B

AV4rziFj…QhTLsLyZ ANscdPEm…b8DYdwDD AeckU1Kq…a9chH61d AN4upMPL…NCifBT7h APLQwRb1…uLY8teft

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.

1.000 × 10⁹⁵(96-digit number)

10009652262996238091…78954335386150912319

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

1.000 × 10⁹⁵(96-digit number)

10009652262996238091…78954335386150912319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.000 × 10⁹⁵(96-digit number)

10009652262996238091…78954335386150912321

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

2.001 × 10⁹⁵(96-digit number)

20019304525992476182…57908670772301824639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.001 × 10⁹⁵(96-digit number)

20019304525992476182…57908670772301824641

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

4.003 × 10⁹⁵(96-digit number)

40038609051984952364…15817341544603649279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.003 × 10⁹⁵(96-digit number)

40038609051984952364…15817341544603649281

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

8.007 × 10⁹⁵(96-digit number)

80077218103969904728…31634683089207298559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.007 × 10⁹⁵(96-digit number)

80077218103969904728…31634683089207298561

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

1.601 × 10⁹⁶(97-digit number)

16015443620793980945…63269366178414597119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.601 × 10⁹⁶(97-digit number)

16015443620793980945…63269366178414597121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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