Block #324,710

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 12:48:17 PM · Difficulty 10.2067 · 6,471,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4e609d028a940451866c657210182f6c58a767075a345817de5203456e6c434

View on Chainz ↗

Height

#324,710

Difficulty

10.206654

Transactions

Size

1.66 KB

Version

Bits

0a34e74c

Nonce

11,809

Timestamp

12/22/2013, 12:48:17 PM

Confirmations

6,471,464

Mined by

⛏️ P2SHAQicfNxAndNBekCr47TWQT3YksVAvFE44J

Merkle Root

3d9daf077aa3aef66c9a0325ab13ae44f6d0766df0a4708b3512700b418d9d03

Transactions (5)

Coinbase9f9763bd856e9b…5d3463a6e62e05

1 in → 1 out9.6200 XPM109 B

AQicfNxA…VAvFE44J

36f33fa0d11d14…8d1a8c3e46e014

2 in → 2 out69.4344 XPM374 B

AbtXW5Bv…A6bQQiUc AVNPLrP4…xpsFYcon

ec663c02371458…ab7e5fc7ebd934

4 in → 2 out10.0933 XPM671 B

AeH9tshU…fbg4NJnW AZwyMUeE…rxMQeLU7

1aa0a213a70a8a…38cf7fa0448e1f

1 in → 2 out1.5212 XPM226 B

AYvnYHFK…Bu5a2u3K ATcdsJng…qLMnoKZB

d6f1972ab1f8b2…a11560dc59d64c

1 in → 2 out1.4762 XPM227 B

ASTXicGA…V1vGz5RK ALjnxG1T…SjTDMRi8

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.

8.400 × 10⁸⁹(90-digit number)

84006884309059635664…97544331967989583999

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

8.400 × 10⁸⁹(90-digit number)

84006884309059635664…97544331967989583999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.400 × 10⁸⁹(90-digit number)

84006884309059635664…97544331967989584001

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

1.680 × 10⁹⁰(91-digit number)

16801376861811927132…95088663935979167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.680 × 10⁹⁰(91-digit number)

16801376861811927132…95088663935979168001

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

3.360 × 10⁹⁰(91-digit number)

33602753723623854265…90177327871958335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.360 × 10⁹⁰(91-digit number)

33602753723623854265…90177327871958336001

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

6.720 × 10⁹⁰(91-digit number)

67205507447247708531…80354655743916671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.720 × 10⁹⁰(91-digit number)

67205507447247708531…80354655743916672001

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

1.344 × 10⁹¹(92-digit number)

13441101489449541706…60709311487833343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.344 × 10⁹¹(92-digit number)

13441101489449541706…60709311487833344001

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