Block #2,395,262

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2017, 10:40:26 PM · Difficulty 10.8732 · 4,446,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e009d23900d7482a95b21a19202d7bdf43167fd53789e429f8a3059207dcc5c

View on Chainz ↗

Height

#2,395,262

Difficulty

10.873229

Transactions

Size

721 B

Version

Bits

0adf8be9

Nonce

117,589,923

Timestamp

11/25/2017, 10:40:26 PM

Confirmations

4,446,318

Mined by

⛏️ P2SHAe4t5pM3tuWjSnt32H3j5rQUAvTNdKWKXT

Merkle Root

d9739a0ca6e7b543761b6134c4b84080dea4f60a1d825373577e5983cda8baef

Transactions (2)

Coinbaseaa3491a1105d5a…83c8e6f5957022

1 in → 1 out8.4500 XPM109 B

Ae4t5pM3…TNdKWKXT

5c04a488e466f8…5e7ca184b17097

3 in → 2 out1206.8489 XPM522 B

AM5AA3Dj…NCsfvYt2 AZ7xo3ni…aXTAFhZR

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.

6.474 × 10⁹³(94-digit number)

64749826183322194797…44754681945532659199

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

6.474 × 10⁹³(94-digit number)

64749826183322194797…44754681945532659199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.474 × 10⁹³(94-digit number)

64749826183322194797…44754681945532659201

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

1.294 × 10⁹⁴(95-digit number)

12949965236664438959…89509363891065318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.294 × 10⁹⁴(95-digit number)

12949965236664438959…89509363891065318401

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

2.589 × 10⁹⁴(95-digit number)

25899930473328877918…79018727782130636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.589 × 10⁹⁴(95-digit number)

25899930473328877918…79018727782130636801

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

5.179 × 10⁹⁴(95-digit number)

51799860946657755837…58037455564261273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.179 × 10⁹⁴(95-digit number)

51799860946657755837…58037455564261273601

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

1.035 × 10⁹⁵(96-digit number)

10359972189331551167…16074911128522547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.035 × 10⁹⁵(96-digit number)

10359972189331551167…16074911128522547201

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 #2,395,262

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