Block #2,148,324

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/6/2017, 9:23:28 AM · Difficulty 10.8953 · 4,694,938 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6731de90e88a06a83923479fb9474f85949a698174e1471ffd8b9395d17a6705

View on Chainz ↗

Height

#2,148,324

Difficulty

10.895305

Transactions

Size

878 B

Version

Bits

0ae532b6

Nonce

1,675,631,033

Timestamp

6/6/2017, 9:23:28 AM

Confirmations

4,694,938

Mined by

⛏️ P2SHAdNDrEUncXsLAjwySeHK9HbqgXFMPjDnik

Merkle Root

24701f29f667dac818290ec868786b700dda73085de8b08c0cb17d7402238a80

Transactions (4)

Coinbase59c48330d3832c…0e91e3afe11552

1 in → 1 out8.4400 XPM110 B

AdNDrEUn…FMPjDnik

2806ecf388c8aa…c8c2a7a5fdf611

1 in → 2 out76152.0422 XPM226 B

AS1FQFPb…EZ1ibmQL AZQWzGQr…KkRTMC63

3ee2082a4354d1…62f1b799744fce

1 in → 2 out75535.2622 XPM226 B

AQWi7ndP…4jCaYuiY AHp8dQSj…ioYXnoeQ

f1bd2f12f7e009…a0a33e71f386b7

1 in → 2 out11067.4422 XPM226 B

AcnkmLZa…3ZMiJdUd AVekZgJj…YjeSj8Gp

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.

1.262 × 10⁹⁴(95-digit number)

12624889040008746933…25203139896221085809

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

1.262 × 10⁹⁴(95-digit number)

12624889040008746933…25203139896221085809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.262 × 10⁹⁴(95-digit number)

12624889040008746933…25203139896221085811

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

2.524 × 10⁹⁴(95-digit number)

25249778080017493866…50406279792442171619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.524 × 10⁹⁴(95-digit number)

25249778080017493866…50406279792442171621

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

5.049 × 10⁹⁴(95-digit number)

50499556160034987732…00812559584884343239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.049 × 10⁹⁴(95-digit number)

50499556160034987732…00812559584884343241

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

1.009 × 10⁹⁵(96-digit number)

10099911232006997546…01625119169768686479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.009 × 10⁹⁵(96-digit number)

10099911232006997546…01625119169768686481

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

2.019 × 10⁹⁵(96-digit number)

20199822464013995093…03250238339537372959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.019 × 10⁹⁵(96-digit number)

20199822464013995093…03250238339537372961

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 #2,148,324

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