Block #454,735

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/22/2014, 3:49:31 AM · Difficulty 10.3968 · 6,387,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1641cca2f849662d2f6c97aa2587af1c5db999a7da63bd9eb66ca788c9a85a18

View on Chainz ↗

Height

#454,735

Difficulty

10.396789

Transactions

Size

1005 B

Version

Bits

0a6593f9

Nonce

246,295

Timestamp

3/22/2014, 3:49:31 AM

Confirmations

6,387,292

Mined by

⛏️ OaS-AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5b4c1b0a5b21e11caca8c0ee5c871f3ecf5c461449671f090487d9176feab7b8

Transactions (1)

Coinbase5b4c1b0a5b21e1…87d9176feab7b8

1 in → 25 out9.2400 XPM913 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

7.791 × 10⁹⁸(99-digit number)

77912571575668191926…74408364633686028799

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

7.791 × 10⁹⁸(99-digit number)

77912571575668191926…74408364633686028799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.791 × 10⁹⁸(99-digit number)

77912571575668191926…74408364633686028801

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

1.558 × 10⁹⁹(100-digit number)

15582514315133638385…48816729267372057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.558 × 10⁹⁹(100-digit number)

15582514315133638385…48816729267372057601

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

3.116 × 10⁹⁹(100-digit number)

31165028630267276770…97633458534744115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.116 × 10⁹⁹(100-digit number)

31165028630267276770…97633458534744115201

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

6.233 × 10⁹⁹(100-digit number)

62330057260534553540…95266917069488230399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.233 × 10⁹⁹(100-digit number)

62330057260534553540…95266917069488230401

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

1.246 × 10¹⁰⁰(101-digit number)

12466011452106910708…90533834138976460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.246 × 10¹⁰⁰(101-digit number)

12466011452106910708…90533834138976460801

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

2.493 × 10¹⁰⁰(101-digit number)

24932022904213821416…81067668277952921599

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 #454,735

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