Block #453,045

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 11:56:22 PM · Difficulty 10.3939 · 6,363,934 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ef1247d9ecbab5242fbdbae08316b9eaf272fe30c22ae85952cd26290b0c9d5

View on Chainz ↗

Height

#453,045

Difficulty

10.393881

Transactions

Size

1005 B

Version

Bits

0a64d568

Nonce

75,437

Timestamp

3/20/2014, 11:56:22 PM

Confirmations

6,363,934

Mined by

⛏️ FAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

2d10b961de299eece33c65d9103aaa075df36684d4f4d59f7ee7e2d580fe5045

Transactions (2)

Coinbase07ac6c92fec0ed…d915c9b358791b

1 in → 17 out9.2500 XPM641 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg Adbb4svj…dQWTHsq5 AXVLciVJ…uTVo9CdN AGz9gyZW…bo8NYQpw

df77751cb886ba…42ba60b93ed4f2

2 in → 1 out18.7200 XPM272 B

Aa7SCWJe…EEUE2cR6

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.

4.300 × 10⁹⁹(100-digit number)

43006863542625699977…71587728426751940449

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

4.300 × 10⁹⁹(100-digit number)

43006863542625699977…71587728426751940449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.300 × 10⁹⁹(100-digit number)

43006863542625699977…71587728426751940451

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

8.601 × 10⁹⁹(100-digit number)

86013727085251399955…43175456853503880899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.601 × 10⁹⁹(100-digit number)

86013727085251399955…43175456853503880901

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

1.720 × 10¹⁰⁰(101-digit number)

17202745417050279991…86350913707007761799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.720 × 10¹⁰⁰(101-digit number)

17202745417050279991…86350913707007761801

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

3.440 × 10¹⁰⁰(101-digit number)

34405490834100559982…72701827414015523599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.440 × 10¹⁰⁰(101-digit number)

34405490834100559982…72701827414015523601

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

6.881 × 10¹⁰⁰(101-digit number)

68810981668201119964…45403654828031047199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.881 × 10¹⁰⁰(101-digit number)

68810981668201119964…45403654828031047201

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 #453,045

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