Block #398,347

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 4:11:17 PM · Difficulty 10.4242 · 6,407,490 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4587b817fce6d0ee42ceda1aff9759493f24002785cfc5c782642e5e9a944b0

View on Chainz ↗

Height

#398,347

Difficulty

10.424248

Transactions

Size

1.17 KB

Version

Bits

0a6c9b84

Nonce

334,960

Timestamp

2/10/2014, 4:11:17 PM

Confirmations

6,407,490

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

cd11e071826df27b40f7dafcfa93924367f9aea071ae5c879a796948fcf5aed7

Transactions (2)

Coinbase04221ba809ace8…0a3fb4112ca13b

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 AXX1wTMN…FfSE8V61 AJzWx2VD…j4ZSMit5

ab028e4dd79646…a6c88b52ceab7d

1 in → 2 out2999.9900 XPM227 B

AZr2Eu59…ismTGcLC AQqna1Wb…K4EHTtSN

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.

6.975 × 10⁹⁷(98-digit number)

69755290578762487956…20254949569749274559

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

6.975 × 10⁹⁷(98-digit number)

69755290578762487956…20254949569749274559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.975 × 10⁹⁷(98-digit number)

69755290578762487956…20254949569749274561

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

1.395 × 10⁹⁸(99-digit number)

13951058115752497591…40509899139498549119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.395 × 10⁹⁸(99-digit number)

13951058115752497591…40509899139498549121

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

2.790 × 10⁹⁸(99-digit number)

27902116231504995182…81019798278997098239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.790 × 10⁹⁸(99-digit number)

27902116231504995182…81019798278997098241

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

5.580 × 10⁹⁸(99-digit number)

55804232463009990365…62039596557994196479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.580 × 10⁹⁸(99-digit number)

55804232463009990365…62039596557994196481

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

1.116 × 10⁹⁹(100-digit number)

11160846492601998073…24079193115988392959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.116 × 10⁹⁹(100-digit number)

11160846492601998073…24079193115988392961

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