Block #2,735,860

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/6/2018, 1:21:02 AM · Difficulty 11.6105 · 4,105,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f684d2ea331405b1400af33407f242d0383c01b78a3d38a505e8a7ac2fcf477

View on Chainz ↗

Height

#2,735,860

Difficulty

11.610491

Transactions

Size

1.36 KB

Version

Bits

0b9c491f

Nonce

752,111,064

Timestamp

7/6/2018, 1:21:02 AM

Confirmations

4,105,167

Mined by

⛏️ P2SHAG47ed25EoVP2cP9B9cmBvPREoub4ammKN

Merkle Root

0565be130ff06e89b4f20b23bdaf6674f11d22f1ea5d679fc0593e1510d4b004

Transactions (3)

Coinbaseffad3fab594b1a…ee803ab9211586

1 in → 1 out7.4300 XPM110 B

AG47ed25…ub4ammKN

75de9b6aa17177…c21b6a4ae5480e

2 in → 2 out3.1546 XPM375 B

AXbEFkEE…J67sPzeK AJ69hN3S…WJyH9SH3

f8fc95d5b96b2a…8fea4e70fba515

5 in → 2 out0.1192 XPM819 B

AQjQFWcf…2gpf2Pct AN7b55gz…YroqkbjU

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.

3.267 × 10⁹⁵(96-digit number)

32673134310600611366…13668908284465036159

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

3.267 × 10⁹⁵(96-digit number)

32673134310600611366…13668908284465036159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.267 × 10⁹⁵(96-digit number)

32673134310600611366…13668908284465036161

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

6.534 × 10⁹⁵(96-digit number)

65346268621201222732…27337816568930072319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.534 × 10⁹⁵(96-digit number)

65346268621201222732…27337816568930072321

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

1.306 × 10⁹⁶(97-digit number)

13069253724240244546…54675633137860144639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.306 × 10⁹⁶(97-digit number)

13069253724240244546…54675633137860144641

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

2.613 × 10⁹⁶(97-digit number)

26138507448480489093…09351266275720289279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.613 × 10⁹⁶(97-digit number)

26138507448480489093…09351266275720289281

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

5.227 × 10⁹⁶(97-digit number)

52277014896960978186…18702532551440578559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.227 × 10⁹⁶(97-digit number)

52277014896960978186…18702532551440578561

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.045 × 10⁹⁷(98-digit number)

10455402979392195637…37405065102881157119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,735,860

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