Block #323,213

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 12:16:09 PM · Difficulty 10.2026 · 6,494,096 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b123fcf9a58ccbd48a8142a7d2ee0b7f2c89b59c22f137d302c0026c08ee707f

View on Chainz ↗

Height

#323,213

Difficulty

10.202595

Transactions

Size

2.18 KB

Version

Bits

0a33dd43

Nonce

119,558

Timestamp

12/21/2013, 12:16:09 PM

Confirmations

6,494,096

Mined by

⛏️ aRsAdDH1inUX9Em5VtHb8FeNNMUCiKWPvb5kJ

Merkle Root

602625ccfb16679c7c22128b47542cd6f398ba5e2ec7da70e36239a13e43de0b

Transactions (4)

Coinbasec2aefd5128c6cc…9a7ea8f26f448c

1 in → 21 out9.5900 XPM777 B

AdDH1inU…KWPvb5kJ AdqM6VG8…Y9Nf7fmL AWCVEa7p…3vPBmiA2 AZ2pPuKg…95SN2Yr7 AG5YAjec…VhA4Aeh1

8b1c0f30c8c3f4…8230c0b5caf4fa

4 in → 13 out38.7301 XPM909 B

AWBjEfff…ZhirBNJR AdSXFDPP…ANJyvdi7 APEdUQu5…t45s5qQU AKQH1EGy…UXFYqRVr AeKNrjNj…1NEq95Ta

10045efe3e9298…8c9dcb6536b8f4

1 in → 2 out7.5981 XPM227 B

ALiYebHp…nETnU5yT AeHPPH5F…XJzQ1Wio

dd74852aa324b4…290fa8e191bf02

1 in → 2 out7.5677 XPM227 B

AHD9JEy9…nbnrHVhD APyCJcr1…QAhukZCb

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.

1.201 × 10⁹⁸(99-digit number)

12015676565921121384…37138065991931945399

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

1.201 × 10⁹⁸(99-digit number)

12015676565921121384…37138065991931945399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.201 × 10⁹⁸(99-digit number)

12015676565921121384…37138065991931945401

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

2.403 × 10⁹⁸(99-digit number)

24031353131842242768…74276131983863890799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.403 × 10⁹⁸(99-digit number)

24031353131842242768…74276131983863890801

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

4.806 × 10⁹⁸(99-digit number)

48062706263684485536…48552263967727781599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.806 × 10⁹⁸(99-digit number)

48062706263684485536…48552263967727781601

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

9.612 × 10⁹⁸(99-digit number)

96125412527368971072…97104527935455563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.612 × 10⁹⁸(99-digit number)

96125412527368971072…97104527935455563201

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

1.922 × 10⁹⁹(100-digit number)

19225082505473794214…94209055870911126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.922 × 10⁹⁹(100-digit number)

19225082505473794214…94209055870911126401

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 #323,213

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