Block #331,099

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 3:52:48 AM · Difficulty 10.1657 · 6,477,952 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b9ac561d525dc7cea2bc0a6db9899d9bb6ad7cd853a4c368e0199b5d1529cb8

View on Chainz ↗

Height

#331,099

Difficulty

10.165693

Transactions

Size

1.05 KB

Version

Bits

0a2a6ad8

Nonce

39,520

Timestamp

12/27/2013, 3:52:48 AM

Confirmations

6,477,952

Mined by

⛏️ aRNAMR1zc5TKqLrypBMDE8gTfU7Xebj5fokRu

Merkle Root

6675168378d474d9f931c861fad6aa7d23575b60032ec73b621533d36792b672

Transactions (1)

Coinbase6675168378d474…1533d36792b672

1 in → 27 out9.6600 XPM981 B

AMR1zc5T…bj5fokRu AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 APT7p5Sr…fxnkiv5f AJzWx2VD…j4ZSMit5

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.

6.909 × 10⁹⁹(100-digit number)

69098513913219150297…59802102429313356499

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

6.909 × 10⁹⁹(100-digit number)

69098513913219150297…59802102429313356499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.909 × 10⁹⁹(100-digit number)

69098513913219150297…59802102429313356501

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

1.381 × 10¹⁰⁰(101-digit number)

13819702782643830059…19604204858626712999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.381 × 10¹⁰⁰(101-digit number)

13819702782643830059…19604204858626713001

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

2.763 × 10¹⁰⁰(101-digit number)

27639405565287660119…39208409717253425999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.763 × 10¹⁰⁰(101-digit number)

27639405565287660119…39208409717253426001

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

5.527 × 10¹⁰⁰(101-digit number)

55278811130575320238…78416819434506851999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.527 × 10¹⁰⁰(101-digit number)

55278811130575320238…78416819434506852001

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

1.105 × 10¹⁰¹(102-digit number)

11055762226115064047…56833638869013703999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.105 × 10¹⁰¹(102-digit number)

11055762226115064047…56833638869013704001

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 #331,099

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