Block #2,178,514

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/26/2017, 3:46:36 AM · Difficulty 10.9264 · 4,636,520 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d529a5e44b1717c3898eee6d7d8eb985c18f7751ffc4903517920500cb9539d3

View on Chainz ↗

Height

#2,178,514

Difficulty

10.926417

Transactions

Size

948 B

Version

Bits

0aed29b2

Nonce

163,169,679

Timestamp

6/26/2017, 3:46:36 AM

Confirmations

4,636,520

Mined by

⛏️ P2SHAbQ6ykgeiX8UL9FjZKQbYCbiMy7hrwWoCL

Merkle Root

90c093956ccd3fdd3745b4513679c77d313f5ee9e45b8f36114c163b4e87871c

Transactions (3)

Coinbase4ca5abcb4ccfc9…a53270cfdbc4bc

1 in → 1 out8.3800 XPM110 B

AbQ6ykge…7hrwWoCL

5df4d151a98699…935be604ab1937

3 in → 2 out372.6615 XPM523 B

AVB8Kqgj…zUanL8Tf AVhodigr…rtx8r5GP

211969b5153fd6…a4d3109f1a24dd

1 in → 2 out93147.8487 XPM225 B

AS9c1zUB…kZhnLASL AG16bT31…9g9vnA7C

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.

2.088 × 10⁹⁴(95-digit number)

20886870593876600879…33456336370341389299

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

2.088 × 10⁹⁴(95-digit number)

20886870593876600879…33456336370341389299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.088 × 10⁹⁴(95-digit number)

20886870593876600879…33456336370341389301

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

4.177 × 10⁹⁴(95-digit number)

41773741187753201759…66912672740682778599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.177 × 10⁹⁴(95-digit number)

41773741187753201759…66912672740682778601

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

8.354 × 10⁹⁴(95-digit number)

83547482375506403519…33825345481365557199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.354 × 10⁹⁴(95-digit number)

83547482375506403519…33825345481365557201

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

1.670 × 10⁹⁵(96-digit number)

16709496475101280703…67650690962731114399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.670 × 10⁹⁵(96-digit number)

16709496475101280703…67650690962731114401

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

3.341 × 10⁹⁵(96-digit number)

33418992950202561407…35301381925462228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.341 × 10⁹⁵(96-digit number)

33418992950202561407…35301381925462228801

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

6.683 × 10⁹⁵(96-digit number)

66837985900405122815…70602763850924457599

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 #2,178,514

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