Block #421,635

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 4:59:28 AM · Difficulty 10.3730 · 6,387,719 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a3dd617da660600f1fb58ec97c42fd9a6249a57db007197c4e1fd387c91ea9a

View on Chainz ↗

Height

#421,635

Difficulty

10.373033

Transactions

Size

3.45 KB

Version

Bits

0a5f7f1f

Nonce

2,097

Timestamp

2/27/2014, 4:59:28 AM

Confirmations

6,387,719

Mined by

⛏️ P2SHAUMMTB5NwPQNvJxTvLVYWyEYFskEjbv3x6

Merkle Root

84706ce5cc04f83c4a4d5b6018f1a85d2a48b1c43c12921dd733dee0f62bbfb1

Transactions (2)

Coinbase831feb7ecde503…098191ed1d2f0d

1 in → 1 out9.3200 XPM109 B

AUMMTB5N…kEjbv3x6

f88bb6a274c30a…b33ae8b9c6bd21

22 in → 2 out67.5421 XPM3.25 KB

AbTAovh7…ac7Ajgk3 AeLrGpbK…cSAMkB86

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.

1.349 × 10¹⁰⁰(101-digit number)

13497048089860622220…10772114997993960699

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

1.349 × 10¹⁰⁰(101-digit number)

13497048089860622220…10772114997993960699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.349 × 10¹⁰⁰(101-digit number)

13497048089860622220…10772114997993960701

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

2.699 × 10¹⁰⁰(101-digit number)

26994096179721244440…21544229995987921399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.699 × 10¹⁰⁰(101-digit number)

26994096179721244440…21544229995987921401

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

5.398 × 10¹⁰⁰(101-digit number)

53988192359442488880…43088459991975842799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.398 × 10¹⁰⁰(101-digit number)

53988192359442488880…43088459991975842801

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

1.079 × 10¹⁰¹(102-digit number)

10797638471888497776…86176919983951685599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.079 × 10¹⁰¹(102-digit number)

10797638471888497776…86176919983951685601

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

2.159 × 10¹⁰¹(102-digit number)

21595276943776995552…72353839967903371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.159 × 10¹⁰¹(102-digit number)

21595276943776995552…72353839967903371201

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 #421,635

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