Block #310,273

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 12:03:06 AM · Difficulty 9.9951 · 6,497,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ab37020f8bb24cbdf2cfdf4a13a3835580af78d13d323cf9824fc426213bead

View on Chainz ↗

Height

#310,273

Difficulty

9.995126

Transactions

Size

1.21 KB

Version

Bits

09fec08c

Nonce

166,887

Timestamp

12/14/2013, 12:03:06 AM

Confirmations

6,497,426

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

2bf4ae0f058df1366510c03c46c4a4b129227697e755d9fcc8d1f2135fa87e5d

Transactions (1)

Coinbase2bf4ae0f058df1…d1f2135fa87e5d

1 in → 32 out9.9700 XPM1.12 KB

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AFqKfjez…qX9Ace3g Acskt6D1…Db4ci1L8 AcM3ext6…Hwtj9Qp3

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.

2.017 × 10⁹⁵(96-digit number)

20178345034536368719…84818487023736422399

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

2.017 × 10⁹⁵(96-digit number)

20178345034536368719…84818487023736422399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.017 × 10⁹⁵(96-digit number)

20178345034536368719…84818487023736422401

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

4.035 × 10⁹⁵(96-digit number)

40356690069072737439…69636974047472844799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.035 × 10⁹⁵(96-digit number)

40356690069072737439…69636974047472844801

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

8.071 × 10⁹⁵(96-digit number)

80713380138145474879…39273948094945689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.071 × 10⁹⁵(96-digit number)

80713380138145474879…39273948094945689601

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

1.614 × 10⁹⁶(97-digit number)

16142676027629094975…78547896189891379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.614 × 10⁹⁶(97-digit number)

16142676027629094975…78547896189891379201

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

3.228 × 10⁹⁶(97-digit number)

32285352055258189951…57095792379782758399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #310,273

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