Block #2,851,290

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/23/2018, 12:16:19 AM · Difficulty 11.7273 · 3,975,893 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05934d666e57458f2296bb03e80d7e2b25f7e17d379e8738be00ae3a2cdcd527

View on Chainz ↗

Height

#2,851,290

Difficulty

11.727332

Transactions

Size

22.97 KB

Version

Bits

0bba3276

Nonce

2,043,422,969

Timestamp

9/23/2018, 12:16:19 AM

Confirmations

3,975,893

Mined by

⛏️ P2SHATA4SSmnhSKwBEvebK5cZhUeBRAdMnR88c

Merkle Root

815e1a6aed436ded6e0812f23a64f708b95864c838ee845912386202e4fbdc44

Transactions (2)

Coinbase050d0e47a523cf…86ab373d03aded

1 in → 1 out7.5000 XPM110 B

ATA4SSmn…AdMnR88c

d529d1f778a729…ea288d9c2009d7

157 in → 2 out15000.0000 XPM22.77 KB

ALWVCWfS…LPpxkLmP ALnSsKrY…TDGzg7KC

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.

8.428 × 10⁹⁵(96-digit number)

84287867789761647223…77733560570891715359

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

8.428 × 10⁹⁵(96-digit number)

84287867789761647223…77733560570891715359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.428 × 10⁹⁵(96-digit number)

84287867789761647223…77733560570891715361

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

1.685 × 10⁹⁶(97-digit number)

16857573557952329444…55467121141783430719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.685 × 10⁹⁶(97-digit number)

16857573557952329444…55467121141783430721

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

3.371 × 10⁹⁶(97-digit number)

33715147115904658889…10934242283566861439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.371 × 10⁹⁶(97-digit number)

33715147115904658889…10934242283566861441

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

6.743 × 10⁹⁶(97-digit number)

67430294231809317778…21868484567133722879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.743 × 10⁹⁶(97-digit number)

67430294231809317778…21868484567133722881

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

1.348 × 10⁹⁷(98-digit number)

13486058846361863555…43736969134267445759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.348 × 10⁹⁷(98-digit number)

13486058846361863555…43736969134267445761

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

2.697 × 10⁹⁷(98-digit number)

26972117692723727111…87473938268534891519

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 #2,851,290

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