Block #2,152,505

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/9/2017, 1:46:32 AM · Difficulty 10.9018 · 4,690,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4fe249b548146823f4448312dfc8038ee51a4968c035a08e58c31b1b5dfa0286

View on Chainz ↗

Height

#2,152,505

Difficulty

10.901821

Transactions

Size

881 B

Version

Bits

0ae6ddba

Nonce

480,503,974

Timestamp

6/9/2017, 1:46:32 AM

Confirmations

4,690,989

Mined by

⛏️ P2SHAUrVZm1XWWyjSrwW5bnE2UDWGY7Q4n2aEv

Merkle Root

d778daefb1106ae0963243bb3e47ac678b2740dcfbef6a40ff2f7861220f5e2d

Transactions (4)

Coinbaseb634ca5f311b67…f225b77892e0d0

1 in → 1 out8.4300 XPM110 B

AUrVZm1X…7Q4n2aEv

260556fc6cd810…753af3d1e0b0a5

1 in → 2 out6807.9034 XPM227 B

ASTdQZAs…rorQaw6U AXdR6eRX…gLmh2i3w

3b8bebc2b1c8a3…51cce967cc4d93

1 in → 2 out8020.9600 XPM227 B

AUx9TQBN…kHAN4y7s AV6GVuy1…YKkdVbyz

e64e846ef2d0df…77cd0d9c21e0bd

1 in → 2 out3.9814 XPM226 B

ANPiqp6d…dikfvu62 Aer3XYnt…gMPZiVds

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.

1.316 × 10⁹⁶(97-digit number)

13167358290818358019…66502591899141429759

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

1.316 × 10⁹⁶(97-digit number)

13167358290818358019…66502591899141429759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.316 × 10⁹⁶(97-digit number)

13167358290818358019…66502591899141429761

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

2.633 × 10⁹⁶(97-digit number)

26334716581636716038…33005183798282859519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.633 × 10⁹⁶(97-digit number)

26334716581636716038…33005183798282859521

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

5.266 × 10⁹⁶(97-digit number)

52669433163273432077…66010367596565719039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.266 × 10⁹⁶(97-digit number)

52669433163273432077…66010367596565719041

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

1.053 × 10⁹⁷(98-digit number)

10533886632654686415…32020735193131438079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.053 × 10⁹⁷(98-digit number)

10533886632654686415…32020735193131438081

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

2.106 × 10⁹⁷(98-digit number)

21067773265309372830…64041470386262876159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.106 × 10⁹⁷(98-digit number)

21067773265309372830…64041470386262876161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,152,505

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