Block #392,609

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 2:02:46 PM · Difficulty 10.4398 · 6,417,797 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e5bdfe230efc64dc1e16116a44cd363932e43834234aa034e4ed64ce3ae4220

View on Chainz ↗

Height

#392,609

Difficulty

10.439774

Transactions

Size

1.54 KB

Version

Bits

0a709501

Nonce

444,750

Timestamp

2/6/2014, 2:02:46 PM

Confirmations

6,417,797

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f5378b2a9697728c50beff85af3e3babb8e7945f15601d1c1840c16738da0572

Transactions (4)

Coinbase58eb4f8c692bcc…ad56e5ef5a48e1

1 in → 22 out9.1600 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH ATKK7iFz…wZm46KN1

d228232d2da74e…a0c79e4ef3be73

1 in → 2 out4.1495 XPM226 B

AMGWQxaG…LZq89wAX AZrVXBut…USpjEezX

5ecafbd681802d…6267b4747a6f0f

1 in → 2 out2.0971 XPM226 B

AdZqqDHy…wz87ZVHc AcPofLDC…Q92qm7bM

5c1a5ff9f35926…620877b9451a5e

1 in → 2 out2.0546 XPM226 B

Adfs1qLa…mxA8fJYJ AM3dFALc…uLaeH5j4

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.

7.379 × 10⁹³(94-digit number)

73791354202897403743…45998753112738841999

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

7.379 × 10⁹³(94-digit number)

73791354202897403743…45998753112738841999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.379 × 10⁹³(94-digit number)

73791354202897403743…45998753112738842001

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

1.475 × 10⁹⁴(95-digit number)

14758270840579480748…91997506225477683999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.475 × 10⁹⁴(95-digit number)

14758270840579480748…91997506225477684001

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

2.951 × 10⁹⁴(95-digit number)

29516541681158961497…83995012450955367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.951 × 10⁹⁴(95-digit number)

29516541681158961497…83995012450955368001

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

5.903 × 10⁹⁴(95-digit number)

59033083362317922994…67990024901910735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.903 × 10⁹⁴(95-digit number)

59033083362317922994…67990024901910736001

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

1.180 × 10⁹⁵(96-digit number)

11806616672463584598…35980049803821471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.180 × 10⁹⁵(96-digit number)

11806616672463584598…35980049803821472001

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 #392,609

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