Block #2,839,402

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/14/2018, 8:09:58 PM · Difficulty 11.7202 · 4,005,411 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28e339d7d271bbafc70aebea74d68ff5cb2b565be82c6212d6be26bef156752f

View on Chainz ↗

Height

#2,839,402

Difficulty

11.720221

Transactions

Size

2.15 KB

Version

Bits

0bb86067

Nonce

1,730,434,703

Timestamp

9/14/2018, 8:09:58 PM

Confirmations

4,005,411

Mined by

⛏️ P2SHAHMqdN297ko2HK4FBEZFWN1WEKCzGzU5X1

Merkle Root

5c74edd16cf7e07684fd8b625568ebab3633e4c45d0e33db4c40c20b374985a0

Transactions (4)

Coinbasefe6926106604f5…4c5c69835782a1

1 in → 1 out7.3000 XPM110 B

AHMqdN29…CzGzU5X1

a6985fd51f1521…6f17545cde5a14

7 in → 2 out50.9100 XPM875 B

ARezZb4y…FxP7ivbi AZXBBfU5…wFkGWdRt

025509d667b5ff…c325d1abe89a7b

2 in → 2 out14.5300 XPM306 B

AV7eJoTN…pLyuARba ASyJfYVA…vRoXtveR

5831e52ee0b0cd…b998470b9cf7f7

5 in → 2 out4.0404 XPM818 B

AJKaimyM…fRyFMN3k AV3JM4zu…4Yqk98pg

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.

1.326 × 10⁹⁴(95-digit number)

13260291762080312346…49414098140060487679

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

1.326 × 10⁹⁴(95-digit number)

13260291762080312346…49414098140060487679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.326 × 10⁹⁴(95-digit number)

13260291762080312346…49414098140060487681

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

2.652 × 10⁹⁴(95-digit number)

26520583524160624692…98828196280120975359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.652 × 10⁹⁴(95-digit number)

26520583524160624692…98828196280120975361

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

5.304 × 10⁹⁴(95-digit number)

53041167048321249385…97656392560241950719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.304 × 10⁹⁴(95-digit number)

53041167048321249385…97656392560241950721

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

1.060 × 10⁹⁵(96-digit number)

10608233409664249877…95312785120483901439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.060 × 10⁹⁵(96-digit number)

10608233409664249877…95312785120483901441

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

2.121 × 10⁹⁵(96-digit number)

21216466819328499754…90625570240967802879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.121 × 10⁹⁵(96-digit number)

21216466819328499754…90625570240967802881

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

4.243 × 10⁹⁵(96-digit number)

42432933638656999508…81251140481935605759

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 #2,839,402

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