Block #326,873

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 3:35:50 AM · Difficulty 10.1808 · 6,499,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc712675592549a13c5737c3e6570ce01d3ec260bf285377af57cc96f4e5bd95

View on Chainz ↗

Height

#326,873

Difficulty

10.180806

Transactions

Size

210 B

Version

Bits

0a2e4955

Nonce

1,977

Timestamp

12/24/2013, 3:35:50 AM

Confirmations

6,499,173

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a96a710c6980afa64d8172505bbbe50c112cf3e469ec6886954926555e201dcd

Transactions (1)

Coinbasea96a710c6980af…4926555e201dcd

1 in → 1 out9.6300 XPM116 B

AbwWkWZt…kawDhufa

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.

1.531 × 10¹⁰⁴(105-digit number)

15317186855536793373…01741802417532436479

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

1.531 × 10¹⁰⁴(105-digit number)

15317186855536793373…01741802417532436479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.531 × 10¹⁰⁴(105-digit number)

15317186855536793373…01741802417532436481

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

3.063 × 10¹⁰⁴(105-digit number)

30634373711073586747…03483604835064872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.063 × 10¹⁰⁴(105-digit number)

30634373711073586747…03483604835064872961

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

6.126 × 10¹⁰⁴(105-digit number)

61268747422147173495…06967209670129745919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.126 × 10¹⁰⁴(105-digit number)

61268747422147173495…06967209670129745921

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

1.225 × 10¹⁰⁵(106-digit number)

12253749484429434699…13934419340259491839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.225 × 10¹⁰⁵(106-digit number)

12253749484429434699…13934419340259491841

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

2.450 × 10¹⁰⁵(106-digit number)

24507498968858869398…27868838680518983679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.450 × 10¹⁰⁵(106-digit number)

24507498968858869398…27868838680518983681

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 #326,873

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