Block #408,160

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 11:19:59 AM · Difficulty 10.4308 · 6,401,763 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd4c5785109ca968d7d880922fd898ea1a2789560b5948fe04b925daf626605d

View on Chainz ↗

Height

#408,160

Difficulty

10.430826

Transactions

Size

935 B

Version

Bits

0a6e4aa2

Nonce

229,065

Timestamp

2/17/2014, 11:19:59 AM

Confirmations

6,401,763

Mined by

ATp4jJhsSxZ4c3nv24ZhThTqRXTbSgR8Qb

Merkle Root

8e5b23dcd2043a8826655d593597fb9803776ae16b8d59f954f8e00e16d8eddf

Transactions (1)

Coinbase8e5b23dcd2043a…f8e00e16d8eddf

1 in → 23 out9.1800 XPM845 B

ATp4jJhs…TbSgR8Qb AMW1p9oT…2TzdaZxH AZr7Ptuw…CM4Yw5jq AR8WV4KS…SChNuf3B AcgDwGo8…BBFwbjVo

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.

4.997 × 10⁹⁴(95-digit number)

49971818002647942609…66192528188908675279

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

4.997 × 10⁹⁴(95-digit number)

49971818002647942609…66192528188908675279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.997 × 10⁹⁴(95-digit number)

49971818002647942609…66192528188908675281

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

9.994 × 10⁹⁴(95-digit number)

99943636005295885218…32385056377817350559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.994 × 10⁹⁴(95-digit number)

99943636005295885218…32385056377817350561

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

1.998 × 10⁹⁵(96-digit number)

19988727201059177043…64770112755634701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.998 × 10⁹⁵(96-digit number)

19988727201059177043…64770112755634701121

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

3.997 × 10⁹⁵(96-digit number)

39977454402118354087…29540225511269402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.997 × 10⁹⁵(96-digit number)

39977454402118354087…29540225511269402241

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

7.995 × 10⁹⁵(96-digit number)

79954908804236708174…59080451022538804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.995 × 10⁹⁵(96-digit number)

79954908804236708174…59080451022538804481

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

Block #408,160

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