Block #2,195,051

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/6/2017, 1:54:04 AM · Difficulty 10.9533 · 4,630,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3f2a515fcad62afe37a1e44b912cf1205dc2530f3bc6feea507fb28d7f84547

View on Chainz ↗

Height

#2,195,051

Difficulty

10.953337

Transactions

Size

723 B

Version

Bits

0af40de1

Nonce

42,523,740

Timestamp

7/6/2017, 1:54:04 AM

Confirmations

4,630,512

Mined by

⛏️ P2SHAPougitAfmWYT5GYXPgesYjpECXmrTZnvk

Merkle Root

bd2bb03d2973716bfca6417b59bc219ecf7662cd00d188f7a965d5ef9582ade5

Transactions (2)

Coinbase4c8d32531a9695…371d68291360c6

1 in → 1 out8.3300 XPM109 B

APougitA…XmrTZnvk

bc5123e9893fdd…e044ce4b3e7053

3 in → 2 out982.3991 XPM524 B

ASACpbub…RytiJ5wS AePPR69D…yL5adp7b

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.

5.874 × 10⁹⁴(95-digit number)

58744339184772506350…70875539438221611519

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

5.874 × 10⁹⁴(95-digit number)

58744339184772506350…70875539438221611519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.874 × 10⁹⁴(95-digit number)

58744339184772506350…70875539438221611521

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

1.174 × 10⁹⁵(96-digit number)

11748867836954501270…41751078876443223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.174 × 10⁹⁵(96-digit number)

11748867836954501270…41751078876443223041

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

2.349 × 10⁹⁵(96-digit number)

23497735673909002540…83502157752886446079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.349 × 10⁹⁵(96-digit number)

23497735673909002540…83502157752886446081

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

4.699 × 10⁹⁵(96-digit number)

46995471347818005080…67004315505772892159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.699 × 10⁹⁵(96-digit number)

46995471347818005080…67004315505772892161

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

9.399 × 10⁹⁵(96-digit number)

93990942695636010160…34008631011545784319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.399 × 10⁹⁵(96-digit number)

93990942695636010160…34008631011545784321

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

1.879 × 10⁹⁶(97-digit number)

18798188539127202032…68017262023091568639

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 #2,195,051

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