Block #219,763

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 4:24:35 PM · Difficulty 9.9340 · 6,590,424 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba106153d7618e56d4fa834d40a57228299921e08d7d07f644122b5b46c11887

View on Chainz ↗

Height

#219,763

Difficulty

9.934041

Transactions

Size

4.69 KB

Version

Bits

09ef1d4a

Nonce

289,268

Timestamp

10/20/2013, 4:24:35 PM

Confirmations

6,590,424

Mined by

⛏️ sZRdJVAKtAkKPKRrWEFEm1qrcXMnjpxzuxv6uLiD

Merkle Root

0367c78aa0a686254d739582be4afed37f6704a6ec636b5f2418ab6c60e62481

Transactions (4)

Coinbasefe922ae5762329…2fa0fed93dae86

1 in → 39 out10.1000 XPM1.36 KB

AKtAkKPK…uxv6uLiD AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AdnG9gQ7…N9B7mA2p ARpndEmc…Hg792kEk

f64322bcab4305…518393d70cc01e

17 in → 1 out173.0000 XPM1.93 KB

AQAvQSWZ…C9mFkvux

1e37d859d42665…b31fdfb73f1666

3 in → 2 out2.5100 XPM522 B

ASacxSJo…jF4yZ7M9 AUBYUNvT…ZEAQbuFu

4d733e80f0e043…7879a464fe12cb

5 in → 2 out10.9194 XPM820 B

AP9ktE9A…6dBWbNDH ALL6BtTJ…cp6j3qpk

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.

8.264 × 10⁹⁵(96-digit number)

82648968467232958863…03364452642313164799

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

8.264 × 10⁹⁵(96-digit number)

82648968467232958863…03364452642313164799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.264 × 10⁹⁵(96-digit number)

82648968467232958863…03364452642313164801

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

1.652 × 10⁹⁶(97-digit number)

16529793693446591772…06728905284626329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.652 × 10⁹⁶(97-digit number)

16529793693446591772…06728905284626329601

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

3.305 × 10⁹⁶(97-digit number)

33059587386893183545…13457810569252659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.305 × 10⁹⁶(97-digit number)

33059587386893183545…13457810569252659201

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

6.611 × 10⁹⁶(97-digit number)

66119174773786367090…26915621138505318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.611 × 10⁹⁶(97-digit number)

66119174773786367090…26915621138505318401

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

1.322 × 10⁹⁷(98-digit number)

13223834954757273418…53831242277010636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.322 × 10⁹⁷(98-digit number)

13223834954757273418…53831242277010636801

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 #219,763

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