Block #327,458

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 1:43:31 PM · Difficulty 10.1776 · 6,470,695 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aad837f57767eceb43c091281e95d8d37b9400cd38eb87c51dd4be9457af83be

View on Chainz ↗

Height

#327,458

Difficulty

10.177635

Transactions

Size

428 B

Version

Bits

0a2d797c

Nonce

658,972

Timestamp

12/24/2013, 1:43:31 PM

Confirmations

6,470,695

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f3f2dafc7cd255d016743c62954565ee7b56990cfb3ba0fff85de874d1cdd3d9

Transactions (2)

Coinbase736cc1ad80dfea…cbe081cb4446fa

1 in → 1 out9.6500 XPM110 B

AeKNrjNj…1NEq95Ta

124a39c3e0074e…0830e0630c9754

1 in → 2 out6783.8656 XPM226 B

ATyjfUan…H8ZmY831 AdB9X8g8…JX87QERW

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.

5.241 × 10¹⁰⁰(101-digit number)

52411190953430498799…78792308891294062079

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

5.241 × 10¹⁰⁰(101-digit number)

52411190953430498799…78792308891294062079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.241 × 10¹⁰⁰(101-digit number)

52411190953430498799…78792308891294062081

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

1.048 × 10¹⁰¹(102-digit number)

10482238190686099759…57584617782588124159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.048 × 10¹⁰¹(102-digit number)

10482238190686099759…57584617782588124161

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

2.096 × 10¹⁰¹(102-digit number)

20964476381372199519…15169235565176248319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.096 × 10¹⁰¹(102-digit number)

20964476381372199519…15169235565176248321

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

4.192 × 10¹⁰¹(102-digit number)

41928952762744399039…30338471130352496639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.192 × 10¹⁰¹(102-digit number)

41928952762744399039…30338471130352496641

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

8.385 × 10¹⁰¹(102-digit number)

83857905525488798079…60676942260704993279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.385 × 10¹⁰¹(102-digit number)

83857905525488798079…60676942260704993281

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