Block #2,688,644

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 6/2/2018, 1:38:53 PM · Difficulty 11.6795 · 4,142,999 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de371845f85e1ba7396ad9275a21efc1d36297d0bbe1c3bb40b0756dcb315553

View on Chainz ↗

Height

#2,688,644

Difficulty

11.679537

Transactions

Size

1.47 KB

Version

Bits

0badf62b

Nonce

1,148,366,454

Timestamp

6/2/2018, 1:38:53 PM

Confirmations

4,142,999

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

d3dd9a8c129f7b69a2b323105b3742a8d8b4bf9da64d561ecfa0fa77da94e418

Transactions (3)

Coinbasef6a291a1e918b4…6b023429600d25

1 in → 1 out7.3400 XPM110 B

Adqah8zh…1WwoHJ9t

50428ca56ed25a…6448128cf3ff84

6 in → 2 out44.5510 XPM967 B

AYFEkcAy…H7eeFpDT ARY67Yio…VS88Q8ou

e222b6d75adaaa…116d5977959fc6

2 in → 2 out11.9200 XPM341 B

AeHMQK6w…3FvDjCDg AcXtoaKv…4oXYPT9v

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.

5.428 × 10⁹⁵(96-digit number)

54287091596862722453…94572370917995304959

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

5.428 × 10⁹⁵(96-digit number)

54287091596862722453…94572370917995304959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.428 × 10⁹⁵(96-digit number)

54287091596862722453…94572370917995304961

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

1.085 × 10⁹⁶(97-digit number)

10857418319372544490…89144741835990609919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.085 × 10⁹⁶(97-digit number)

10857418319372544490…89144741835990609921

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

2.171 × 10⁹⁶(97-digit number)

21714836638745088981…78289483671981219839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.171 × 10⁹⁶(97-digit number)

21714836638745088981…78289483671981219841

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

4.342 × 10⁹⁶(97-digit number)

43429673277490177962…56578967343962439679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.342 × 10⁹⁶(97-digit number)

43429673277490177962…56578967343962439681

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

8.685 × 10⁹⁶(97-digit number)

86859346554980355925…13157934687924879359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.685 × 10⁹⁶(97-digit number)

86859346554980355925…13157934687924879361

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

1.737 × 10⁹⁷(98-digit number)

17371869310996071185…26315869375849758719

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.737 × 10⁹⁷(98-digit number)

17371869310996071185…26315869375849758721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,688,644

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