Block #373,405

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 6:59:01 AM · Difficulty 10.4258 · 6,434,477 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb511807ce04c4ab4df2c1a3b0e5aa96a72819e89286fee6c1d750c2b0d448f5

View on Chainz ↗

Height

#373,405

Difficulty

10.425788

Transactions

Size

13.84 KB

Version

Bits

0a6d006b

Nonce

230,793

Timestamp

1/24/2014, 6:59:01 AM

Confirmations

6,434,477

Mined by

⛏️ aRzANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

437f0c9d32f7ef889815eec7255debf164165a62d2f036bf4fb37720b105dd0b

Transactions (4)

Coinbasef6eba6f8da7e7f…34013dfc9c9708

1 in → 1 out9.1900 XPM97 B

ANEZwy9t…E1uf5dKY

350a9ce015c0c3…c9bc71efded9d6

2 in → 2 out100.9830 XPM374 B

Aatv2skd…5gMmqvZp ANBUmewC…rFVRsycu

0c20481cac1b5e…416b447b7b3010

4 in → 2 out25.1025 XPM668 B

Abb6hF9R…Qsv2EQwJ AG2tCmdm…FTdKj9e6

2530f26a1b3e00…a47aa491e0b999

87 in → 2 out500.0100 XPM12.64 KB

AW6Y76rq…ic4BaHcW AJjnK9uC…VreFquR4

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.

1.409 × 10⁹³(94-digit number)

14093761297011657984…00114912586281008159

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

1.409 × 10⁹³(94-digit number)

14093761297011657984…00114912586281008159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.409 × 10⁹³(94-digit number)

14093761297011657984…00114912586281008161

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

2.818 × 10⁹³(94-digit number)

28187522594023315969…00229825172562016319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.818 × 10⁹³(94-digit number)

28187522594023315969…00229825172562016321

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

5.637 × 10⁹³(94-digit number)

56375045188046631939…00459650345124032639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.637 × 10⁹³(94-digit number)

56375045188046631939…00459650345124032641

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

1.127 × 10⁹⁴(95-digit number)

11275009037609326387…00919300690248065279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.127 × 10⁹⁴(95-digit number)

11275009037609326387…00919300690248065281

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

2.255 × 10⁹⁴(95-digit number)

22550018075218652775…01838601380496130559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.255 × 10⁹⁴(95-digit number)

22550018075218652775…01838601380496130561

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 #373,405

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