Block #421,463

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 1:54:49 AM · Difficulty 10.3745 · 6,405,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af915dd83d64da9555f7ccd19c9b868cbd07da7aae2d932f4f84995c6b8b3342

View on Chainz ↗

Height

#421,463

Difficulty

10.374479

Transactions

Size

11.60 KB

Version

Bits

0a5fdddd

Nonce

9,791

Timestamp

2/27/2014, 1:54:49 AM

Confirmations

6,405,257

Mined by

⛏️ WnaSAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

b0fab1bbce9773a66eb8498b20215446d77364b0c0f53436be97bd1f4902a9bd

Transactions (2)

Coinbase81a0b450ffa85c…e1ee9a5ac8befb

1 in → 26 out9.2800 XPM947 B

Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH ANE2UCVG…PjaSyQSy AHrv45cn…srrxPAwx

44c0ec1e97b908…b470325eebd66b

73 in → 1 out24.6228 XPM10.59 KB

ATrZibkv…b2FhWcnZ

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.

4.916 × 10⁹⁶(97-digit number)

49169439785744305733…47833727485483343949

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

4.916 × 10⁹⁶(97-digit number)

49169439785744305733…47833727485483343949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.916 × 10⁹⁶(97-digit number)

49169439785744305733…47833727485483343951

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

9.833 × 10⁹⁶(97-digit number)

98338879571488611466…95667454970966687899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.833 × 10⁹⁶(97-digit number)

98338879571488611466…95667454970966687901

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

1.966 × 10⁹⁷(98-digit number)

19667775914297722293…91334909941933375799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.966 × 10⁹⁷(98-digit number)

19667775914297722293…91334909941933375801

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

3.933 × 10⁹⁷(98-digit number)

39335551828595444586…82669819883866751599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.933 × 10⁹⁷(98-digit number)

39335551828595444586…82669819883866751601

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

7.867 × 10⁹⁷(98-digit number)

78671103657190889173…65339639767733503199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.867 × 10⁹⁷(98-digit number)

78671103657190889173…65339639767733503201

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 #421,463

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