Block #222,457

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 6:19:36 AM · Difficulty 9.9394 · 6,571,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d55ea73d5d7c791ba016461fe1f09019cedcb3963f00714bc6678e62b8c2bf44

View on Chainz ↗

Height

#222,457

Difficulty

9.939430

Transactions

Size

1.54 KB

Version

Bits

09f07e7f

Nonce

313,250

Timestamp

10/22/2013, 6:19:36 AM

Confirmations

6,571,736

Merkle Root

3134ddf1546a011849dcbefe015fc19e2b73b9f82e7afe429eea73c7b6c342d2

Transactions (5)

Coinbase34c4f340640d26…1fdfefb07a8a34

1 in → 1 out10.1500 XPM110 B

AbuU1HhS…JPwsJEbB

d511a00d5127c0…14c5cd76ac1f06

1 in → 1 out10.1700 XPM159 B

AFsMW6dF…Z3wb5bBq

cfe7f105b38390…cba06dc359fce9

4 in → 9 out40.5000 XPM771 B

ATGsirtj…4e6NjLiY AGdYdg5f…ZrePPako AQReECoY…wTuHRPLY AZdxjFDu…2BXPy6Q2 AbuU1HhS…JPwsJEbB

2cf6a3f4b25ff2…b5234c244fa09b

1 in → 2 out8.0950 XPM225 B

AJcwYxzt…ZjGtW5gq AdyHutyy…DdXqQUHn

5b2bca7a531098…5bdc6e8a381874

1 in → 2 out5.7767 XPM226 B

AHRsFdRQ…P8ne2uE4 AeMLmzZE…przickhP

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.

4.057 × 10⁹⁵(96-digit number)

40577412306582725090…68860663976263244799

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

4.057 × 10⁹⁵(96-digit number)

40577412306582725090…68860663976263244799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.057 × 10⁹⁵(96-digit number)

40577412306582725090…68860663976263244801

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

8.115 × 10⁹⁵(96-digit number)

81154824613165450180…37721327952526489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.115 × 10⁹⁵(96-digit number)

81154824613165450180…37721327952526489601

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

1.623 × 10⁹⁶(97-digit number)

16230964922633090036…75442655905052979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.623 × 10⁹⁶(97-digit number)

16230964922633090036…75442655905052979201

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

3.246 × 10⁹⁶(97-digit number)

32461929845266180072…50885311810105958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.246 × 10⁹⁶(97-digit number)

32461929845266180072…50885311810105958401

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

6.492 × 10⁹⁶(97-digit number)

64923859690532360144…01770623620211916799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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