Block #2,750,967

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/16/2018, 5:32:12 AM · Difficulty 11.6446 · 4,082,463 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99a3382ece97ec3fff1fbd332bc788369d16c8080874d7a7f83e6add97f57703

View on Chainz ↗

Height

#2,750,967

Difficulty

11.644628

Transactions

Size

1.96 KB

Version

Bits

0ba5064f

Nonce

1,768,373,637

Timestamp

7/16/2018, 5:32:12 AM

Confirmations

4,082,463

Mined by

⛏️ P2SHAPKjG96nvGrDTjsqB5X8pKK6FfVoyymxAM

Merkle Root

7fa50ebfa62dc1bda50bc908a282b1c53ac9f9bff622c6f483654debae94395c

Transactions (5)

Coinbase59ba330464c1c9…337441f2a2e372

1 in → 1 out7.4000 XPM110 B

APKjG96n…VoyymxAM

c1c668cf28709f…8e9c7582527b5f

4 in → 2 out9.9206 XPM671 B

Aanpbe3s…up4wSyyy AHLPUwXV…p1Q6Denj

0cbbc5ef1ac08d…04d01542a24ba2

2 in → 2 out14.7100 XPM306 B

Ab7ZGkny…PLgHQR2u ASxkQAv4…mZ45Sf5W

958fc8841b32f9…88075c652eaa9f

2 in → 2 out12.0600 XPM340 B

AMEQzuxr…ZaDRrBNQ AH8UAN4u…zxwiJkLN

c326432459b7a4…da43b061202d98

3 in → 2 out10.4500 XPM489 B

AadYtyde…FcTHpFKN AQzi7R5x…CJ6UABkL

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.

8.337 × 10⁹³(94-digit number)

83371790038584347456…00343315795719388829

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

8.337 × 10⁹³(94-digit number)

83371790038584347456…00343315795719388829

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.337 × 10⁹³(94-digit number)

83371790038584347456…00343315795719388831

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

1.667 × 10⁹⁴(95-digit number)

16674358007716869491…00686631591438777659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.667 × 10⁹⁴(95-digit number)

16674358007716869491…00686631591438777661

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

3.334 × 10⁹⁴(95-digit number)

33348716015433738982…01373263182877555319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.334 × 10⁹⁴(95-digit number)

33348716015433738982…01373263182877555321

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

6.669 × 10⁹⁴(95-digit number)

66697432030867477965…02746526365755110639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.669 × 10⁹⁴(95-digit number)

66697432030867477965…02746526365755110641

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

1.333 × 10⁹⁵(96-digit number)

13339486406173495593…05493052731510221279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.333 × 10⁹⁵(96-digit number)

13339486406173495593…05493052731510221281

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

2.667 × 10⁹⁵(96-digit number)

26678972812346991186…10986105463020442559

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 #2,750,967

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