Block #1,074,534

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2015, 2:38:43 AM · Difficulty 10.7438 · 5,734,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3001d711a91dc6bd81523c0cd6aab4c1927af5aeddbabc8822d84e27189140c3

View on Chainz ↗

Height

#1,074,534

Difficulty

10.743848

Transactions

Size

34.50 KB

Version

Bits

0abe6ccb

Nonce

1,135,452,980

Timestamp

5/25/2015, 2:38:43 AM

Confirmations

5,734,444

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e53a0143d85491682e852f3d891ede0cd936b11c5938e7434bc75f7d2c294a4e

Transactions (4)

Coinbase1e70cf7e4982c0…f824a0d0f93355

1 in → 1 out9.0200 XPM116 B

ANSXnLY2…Sd25TjkD

16e398e7339464…4fe33c71e3fa69

233 in → 1 out1499.9900 XPM33.71 KB

ASTskmNr…Nc7pPas2

d2fc22cf6221a8…458c79b70c226d

1 in → 2 out3.7507 XPM227 B

ANMLiEMZ…VLvezaWb Ae7YXEyn…hnSYZsCr

591ba052f338fb…b27eb0fa35773a

2 in → 2 out5.6795 XPM373 B

AZ3fRsoW…RRzQCnDS Aa4PtTwK…H3ppZFzk

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.

7.318 × 10⁹⁷(98-digit number)

73181385677746771934…30339186587622604799

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

7.318 × 10⁹⁷(98-digit number)

73181385677746771934…30339186587622604799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.318 × 10⁹⁷(98-digit number)

73181385677746771934…30339186587622604801

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

1.463 × 10⁹⁸(99-digit number)

14636277135549354386…60678373175245209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.463 × 10⁹⁸(99-digit number)

14636277135549354386…60678373175245209601

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

2.927 × 10⁹⁸(99-digit number)

29272554271098708773…21356746350490419199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.927 × 10⁹⁸(99-digit number)

29272554271098708773…21356746350490419201

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

5.854 × 10⁹⁸(99-digit number)

58545108542197417547…42713492700980838399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.854 × 10⁹⁸(99-digit number)

58545108542197417547…42713492700980838401

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

1.170 × 10⁹⁹(100-digit number)

11709021708439483509…85426985401961676799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.170 × 10⁹⁹(100-digit number)

11709021708439483509…85426985401961676801

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 #1,074,534

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