Block #322,099

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 6:02:25 PM · Difficulty 10.1996 · 6,487,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b59b06464881fc88bfd5776b92d29269fc7af3cdc06e6fc4412f400e9fe6a9a

View on Chainz ↗

Height

#322,099

Difficulty

10.199569

Transactions

Size

1006 B

Version

Bits

0a3316f5

Nonce

9,974

Timestamp

12/20/2013, 6:02:25 PM

Confirmations

6,487,591

Mined by

⛏️ 3aR9sAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

18576c16735131f199260e5ad089c2c55cb4c37555b062078c45c8d3f181bf39

Transactions (1)

Coinbase18576c16735131…45c8d3f181bf39

1 in → 25 out9.6000 XPM913 B

AQwRN8bE…V8PsTcY9 Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 Actx8HRL…1LEiodun AUH8MTP4…tSSjzeSq

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.

1.431 × 10¹⁰¹(102-digit number)

14312941638713223300…77705529041697806719

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

1.431 × 10¹⁰¹(102-digit number)

14312941638713223300…77705529041697806719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.431 × 10¹⁰¹(102-digit number)

14312941638713223300…77705529041697806721

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

2.862 × 10¹⁰¹(102-digit number)

28625883277426446600…55411058083395613439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.862 × 10¹⁰¹(102-digit number)

28625883277426446600…55411058083395613441

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

5.725 × 10¹⁰¹(102-digit number)

57251766554852893200…10822116166791226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.725 × 10¹⁰¹(102-digit number)

57251766554852893200…10822116166791226881

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

1.145 × 10¹⁰²(103-digit number)

11450353310970578640…21644232333582453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.145 × 10¹⁰²(103-digit number)

11450353310970578640…21644232333582453761

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

2.290 × 10¹⁰²(103-digit number)

22900706621941157280…43288464667164907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.290 × 10¹⁰²(103-digit number)

22900706621941157280…43288464667164907521

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 #322,099

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