Block #421,574

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 4:00:38 AM · Difficulty 10.3728 · 6,396,059 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7e2554ad12f4cf59d2b26f211eef5f374ba033cdb1cd8884a37a18730e0d147

View on Chainz ↗

Height

#421,574

Difficulty

10.372751

Transactions

Size

734 B

Version

Bits

0a5f6c9d

Nonce

6,860,062

Timestamp

2/27/2014, 4:00:38 AM

Confirmations

6,396,059

Mined by

⛏️ P2SHAH6A4342oymuKZ1r1TnHsYjQXFeeDbn8BR

Merkle Root

583cf7b6e994b85c2462e49a8a486ccee308e3094f7ac5ef7a595edf21796886

Transactions (3)

Coinbaseab47f60606df1b…6c921d1c5bebb1

1 in → 1 out9.3000 XPM109 B

AH6A4342…eeDbn8BR

0231b026035fd6…8e9ec10a35aa4f

2 in → 1 out9.3400 XPM341 B

AWio7Z4H…BMKGnZu7

8cad9ef2956a5a…2d8c942afcbfae

1 in → 1 out2.9918 XPM193 B

ASZqbHhP…NRYKprQg

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.

1.015 × 10⁹⁷(98-digit number)

10154302949728554479…02514560737499064319

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

1.015 × 10⁹⁷(98-digit number)

10154302949728554479…02514560737499064319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.015 × 10⁹⁷(98-digit number)

10154302949728554479…02514560737499064321

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

2.030 × 10⁹⁷(98-digit number)

20308605899457108959…05029121474998128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.030 × 10⁹⁷(98-digit number)

20308605899457108959…05029121474998128641

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

4.061 × 10⁹⁷(98-digit number)

40617211798914217919…10058242949996257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.061 × 10⁹⁷(98-digit number)

40617211798914217919…10058242949996257281

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

8.123 × 10⁹⁷(98-digit number)

81234423597828435838…20116485899992514559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.123 × 10⁹⁷(98-digit number)

81234423597828435838…20116485899992514561

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

1.624 × 10⁹⁸(99-digit number)

16246884719565687167…40232971799985029119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.624 × 10⁹⁸(99-digit number)

16246884719565687167…40232971799985029121

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 #421,574

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