Block #448,333

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 8:28:16 PM · Difficulty 10.3682 · 6,378,955 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6390870d1bedf89b674600de0dd1a00ca7996adeb7182c8225790bea6c2c8a4e

View on Chainz ↗

Height

#448,333

Difficulty

10.368216

Transactions

Size

971 B

Version

Bits

0a5e4368

Nonce

2,190

Timestamp

3/17/2014, 8:28:16 PM

Confirmations

6,378,955

Mined by

⛏️ MaS'ZwAWMrD5hPqVPmeJjKKdYvZuVuyFZwsoxvZ3

Merkle Root

b15520d4ee3eeb31df22d81532abdc635f1bed86618106be8172d6d0149c6bc4

Transactions (1)

Coinbaseb15520d4ee3eeb…72d6d0149c6bc4

1 in → 24 out9.2900 XPM879 B

AWMrD5hP…ZwsoxvZ3 AScAzqGc…BZ6tV1vJ AKzkYQaQ…zR4FspJZ Aeq4EEPh…JtANMFSA AFutDVqJ…TJTJj6UF

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.

1.235 × 10⁹⁹(100-digit number)

12353122724704624094…60345155468153292799

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

1.235 × 10⁹⁹(100-digit number)

12353122724704624094…60345155468153292799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.235 × 10⁹⁹(100-digit number)

12353122724704624094…60345155468153292801

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

2.470 × 10⁹⁹(100-digit number)

24706245449409248189…20690310936306585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.470 × 10⁹⁹(100-digit number)

24706245449409248189…20690310936306585601

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

4.941 × 10⁹⁹(100-digit number)

49412490898818496379…41380621872613171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.941 × 10⁹⁹(100-digit number)

49412490898818496379…41380621872613171201

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

9.882 × 10⁹⁹(100-digit number)

98824981797636992759…82761243745226342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.882 × 10⁹⁹(100-digit number)

98824981797636992759…82761243745226342401

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

1.976 × 10¹⁰⁰(101-digit number)

19764996359527398551…65522487490452684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.976 × 10¹⁰⁰(101-digit number)

19764996359527398551…65522487490452684801

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 #448,333

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