Block #2,850,879

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/22/2018, 4:36:55 PM · Difficulty 11.7299 · 3,975,680 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5a43dfd945eb9a5172bae8ef5e2cbbb1739a500e735a85b80ebc02978eebeb2a

View on Chainz ↗

Height

#2,850,879

Difficulty

11.729934

Transactions

Size

51.47 KB

Version

Bits

0bbadcf7

Nonce

1,136,962,725

Timestamp

9/22/2018, 4:36:55 PM

Confirmations

3,975,680

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

9791f6dd1bab578c6ef9ad7b5f9d40f007f59ae3d5dd26524199c6905769744e

Transactions (3)

Coinbasef781d6b9cc6400…68fa0abbf6bf30

1 in → 1 out7.8100 XPM109 B

AUMQRepm…tAfKmdW1

c5b69f8aef295d…06ea25574a6b42

353 in → 1 out35544.9866 XPM51.06 KB

AegoibgD…fSUnMf7r

ccdaab2c059318…fee759d10bdb65

1 in → 2 out3.2128 XPM226 B

AKmq3y1G…mFioT2pV Aa1cbLt5…Nf58QkZT

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.

1.114 × 10⁹⁷(98-digit number)

11145093462497211480…61570490588437442559

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

1.114 × 10⁹⁷(98-digit number)

11145093462497211480…61570490588437442559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.114 × 10⁹⁷(98-digit number)

11145093462497211480…61570490588437442561

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

2.229 × 10⁹⁷(98-digit number)

22290186924994422961…23140981176874885119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.229 × 10⁹⁷(98-digit number)

22290186924994422961…23140981176874885121

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

4.458 × 10⁹⁷(98-digit number)

44580373849988845923…46281962353749770239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.458 × 10⁹⁷(98-digit number)

44580373849988845923…46281962353749770241

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

8.916 × 10⁹⁷(98-digit number)

89160747699977691847…92563924707499540479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.916 × 10⁹⁷(98-digit number)

89160747699977691847…92563924707499540481

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

1.783 × 10⁹⁸(99-digit number)

17832149539995538369…85127849414999080959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.783 × 10⁹⁸(99-digit number)

17832149539995538369…85127849414999080961

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

3.566 × 10⁹⁸(99-digit number)

35664299079991076738…70255698829998161919

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 #2,850,879

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