Block #447,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 5:18:36 AM · Difficulty 10.3545 · 6,352,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f9e02630e1fc75e670497b4d7b7887922fc6b8dce1dc360970d1dccb5157902

View on Chainz ↗

Height

#447,320

Difficulty

10.354499

Transactions

Size

3.45 KB

Version

Bits

0a5ac06e

Nonce

75,831

Timestamp

3/17/2014, 5:18:36 AM

Confirmations

6,352,173

Mined by

⛏️ XAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

73a4cad891cd078596760fa3eb21e05a8abe2c9807749985bf17318617f586b0

Transactions (2)

Coinbase8cd324db5dc021…2c2f1ace367f90

1 in → 24 out9.3483 XPM879 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AbPcCMg4…719q6mAX AcuM7XiJ…5uND8Jce

bcf64478c4ce33…0223af3d917997

17 in → 1 out5.2300 XPM2.50 KB

ARhWTc75…r6emZmwX

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.

2.529 × 10⁹⁹(100-digit number)

25294301691554336984…18124677361162393599

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

2.529 × 10⁹⁹(100-digit number)

25294301691554336984…18124677361162393599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.529 × 10⁹⁹(100-digit number)

25294301691554336984…18124677361162393601

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

5.058 × 10⁹⁹(100-digit number)

50588603383108673969…36249354722324787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.058 × 10⁹⁹(100-digit number)

50588603383108673969…36249354722324787201

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

1.011 × 10¹⁰⁰(101-digit number)

10117720676621734793…72498709444649574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.011 × 10¹⁰⁰(101-digit number)

10117720676621734793…72498709444649574401

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

2.023 × 10¹⁰⁰(101-digit number)

20235441353243469587…44997418889299148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.023 × 10¹⁰⁰(101-digit number)

20235441353243469587…44997418889299148801

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

4.047 × 10¹⁰⁰(101-digit number)

40470882706486939175…89994837778598297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.047 × 10¹⁰⁰(101-digit number)

40470882706486939175…89994837778598297601

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