Block #741,184

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/25/2014, 9:31:08 PM · Difficulty 10.9800 · 6,090,325 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a4958df4aa27eb30efb025bde5f5a612ff8a4d29dd3d301fc51a427ceba249e

View on Chainz ↗

Height

#741,184

Difficulty

10.979972

Transactions

Size

1.73 KB

Version

Bits

0afadf74

Nonce

347,322,329

Timestamp

9/25/2014, 9:31:08 PM

Confirmations

6,090,325

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e43a8eda372327294644d98fcc798bbe9c9bc30e3c9967e8b6ef10d6f43b9c80

Transactions (4)

Coinbase8aec2bdd18bf2d…e0df2d536bfacf

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

c7d50c28dc46cf…db9815a7d19828

7 in → 2 out105.0944 XPM1.09 KB

AYM4YTAg…ui8F2YHf AaqUnmzu…8xk9hBiq

5cabf7a689a101…c3f31604f0091d

1 in → 2 out3.3120 XPM225 B

AWeFTqSF…usRDA3NM AdrMa6Xt…AwFJG5Wn

884032c09cd58b…9ad25b90022323

1 in → 2 out2.9830 XPM225 B

AapErjYX…a7jQAgi5 AMoJsji6…a13Bp22Q

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.

5.596 × 10⁹⁷(98-digit number)

55963105257571057659…29949645585033441279

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

5.596 × 10⁹⁷(98-digit number)

55963105257571057659…29949645585033441279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.596 × 10⁹⁷(98-digit number)

55963105257571057659…29949645585033441281

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

1.119 × 10⁹⁸(99-digit number)

11192621051514211531…59899291170066882559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.119 × 10⁹⁸(99-digit number)

11192621051514211531…59899291170066882561

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

2.238 × 10⁹⁸(99-digit number)

22385242103028423063…19798582340133765119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.238 × 10⁹⁸(99-digit number)

22385242103028423063…19798582340133765121

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

4.477 × 10⁹⁸(99-digit number)

44770484206056846127…39597164680267530239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.477 × 10⁹⁸(99-digit number)

44770484206056846127…39597164680267530241

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

8.954 × 10⁹⁸(99-digit number)

89540968412113692254…79194329360535060479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.954 × 10⁹⁸(99-digit number)

89540968412113692254…79194329360535060481

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 #741,184

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