Block #420,818

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 3:07:03 PM · Difficulty 10.3758 · 6,396,285 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

51fc3091a280ae02282f99be2a7667f2606a73e2dd01f23bddb23bb829458587

View on Chainz ↗

Height

#420,818

Difficulty

10.375817

Transactions

Size

1.70 KB

Version

Bits

0a60358c

Nonce

27,584

Timestamp

2/26/2014, 3:07:03 PM

Confirmations

6,396,285

Mined by

⛏️ kAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

3065a3c447ae62a0b54451013dd22d81bf5f8c23d64527d8e8f6798f06a04f38

Transactions (4)

Coinbasedc34459177e117…10ea43dc31de06

1 in → 2 out9.3000 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

fed520e1d512ef…99213bc8e90b78

4 in → 7 out20.3236 XPM770 B

AQufhWCK…onJSt1Rt AcBnBiUw…CYFN81QZ ANL7dupX…BQ491fzW AZ3PWPr3…T7o8gD2E AKc9Rmjx…Bir3N5mm

15a1dd139868a3…b7bc913eb85db3

1 in → 2 out2.3641 XPM226 B

AQqBYtwM…RytyXtuL AQNwqUcd…HqCWbfp7

c374d345c1c943…646a47a4973a49

3 in → 2 out1.0171 XPM522 B

ALtNbVCg…Jy7ZyNEv AdfHhZ6o…6swH6dxw

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.

7.794 × 10¹⁰⁰(101-digit number)

77949419593689251520…44272595873970144799

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

7.794 × 10¹⁰⁰(101-digit number)

77949419593689251520…44272595873970144799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.794 × 10¹⁰⁰(101-digit number)

77949419593689251520…44272595873970144801

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

1.558 × 10¹⁰¹(102-digit number)

15589883918737850304…88545191747940289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.558 × 10¹⁰¹(102-digit number)

15589883918737850304…88545191747940289601

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

3.117 × 10¹⁰¹(102-digit number)

31179767837475700608…77090383495880579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.117 × 10¹⁰¹(102-digit number)

31179767837475700608…77090383495880579201

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

6.235 × 10¹⁰¹(102-digit number)

62359535674951401216…54180766991761158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.235 × 10¹⁰¹(102-digit number)

62359535674951401216…54180766991761158401

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

1.247 × 10¹⁰²(103-digit number)

12471907134990280243…08361533983522316799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.247 × 10¹⁰²(103-digit number)

12471907134990280243…08361533983522316801

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 #420,818

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