Block #392,473

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 11:51:05 AM · Difficulty 10.4388 · 6,400,164 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07f06997884ea471bcbc4ab026f4899c5d6850742f5f8835a596b0059ae51098

View on Chainz ↗

Height

#392,473

Difficulty

10.438756

Transactions

Size

1.51 KB

Version

Bits

0a705258

Nonce

68,548

Timestamp

2/6/2014, 11:51:05 AM

Confirmations

6,400,164

Merkle Root

e0e924712f02da4b7a55b58881a0e8aba2984cf38c090691d51bcb7f5a30ff73

Transactions (5)

Coinbasec527594f6b0129…fe68952086ddb9

1 in → 1 out9.2000 XPM109 B

ATbfdtue…YwyPrhjz

cefdea29375350…9001cbc524302c

1 in → 2 out15815.7939 XPM226 B

AJKDMHjJ…ZWtSKZz9 AWuPu2hr…dijaSzAW

0782156676b50b…c95c57564ff28c

4 in → 2 out25.2408 XPM670 B

AHYqe8HB…B66GyRdb AQdZkpQo…9GyVU1sY

0fffca729be0a0…30ace9a6b782e7

1 in → 2 out7.1664 XPM226 B

AeS88hLZ…AAVfGWkk AeZZPYHj…5K1XcjZJ

21ba0eace02e09…b4ece62472efc9

1 in → 2 out1.1051 XPM227 B

ALmyc36L…7JaEyWnZ AHkFJhyP…6MjqZNDP

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.

4.205 × 10⁹⁸(99-digit number)

42053685292041381273…12312690499630168479

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

4.205 × 10⁹⁸(99-digit number)

42053685292041381273…12312690499630168479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.205 × 10⁹⁸(99-digit number)

42053685292041381273…12312690499630168481

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

8.410 × 10⁹⁸(99-digit number)

84107370584082762546…24625380999260336959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.410 × 10⁹⁸(99-digit number)

84107370584082762546…24625380999260336961

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

1.682 × 10⁹⁹(100-digit number)

16821474116816552509…49250761998520673919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.682 × 10⁹⁹(100-digit number)

16821474116816552509…49250761998520673921

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

3.364 × 10⁹⁹(100-digit number)

33642948233633105018…98501523997041347839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.364 × 10⁹⁹(100-digit number)

33642948233633105018…98501523997041347841

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

6.728 × 10⁹⁹(100-digit number)

67285896467266210036…97003047994082695679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.728 × 10⁹⁹(100-digit number)

67285896467266210036…97003047994082695681

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