Block #400,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2014, 4:01:39 AM · Difficulty 10.4284 · 6,395,874 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58874a1f71da0cfb7496cf50b0153101dfba6f24d5337c6f8037dd5cdebf7e69

View on Chainz ↗

Height

#400,522

Difficulty

10.428417

Transactions

Size

1.11 KB

Version

Bits

0a6dacbd

Nonce

29,022

Timestamp

2/12/2014, 4:01:39 AM

Confirmations

6,395,874

Mined by

⛏️ P2SHAYqEiQrkrrW6WiaBmi4hfyzhJJ4im26qEr

Merkle Root

7ca5ab154dcee915e2f279efda8367084f701f5356665dafc2d1948960abff59

Transactions (4)

Coinbase7e0750f0318a59…cd714e9af47052

1 in → 1 out9.2200 XPM109 B

AYqEiQrk…4im26qEr

cc61ce4784ffd5…2f47deda1bd08f

3 in → 2 out1716.8186 XPM520 B

AS8qNPLp…8bGt6oU7 Aaq5ydQe…MWD3ZPck

4a8f8e35a36b10…46ba4671809b1d

1 in → 1 out2.9916 XPM192 B

AXHwdSLu…fwyTxZ7W

d9aea53fba9db9…ce657797666312

1 in → 2 out0.7300 XPM227 B

ATUhp4r6…uGNomEmi AZAHU1tj…ojTmhpEV

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.

7.282 × 10⁹⁹(100-digit number)

72828610045049463149…59552563980751850629

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

7.282 × 10⁹⁹(100-digit number)

72828610045049463149…59552563980751850629

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.282 × 10⁹⁹(100-digit number)

72828610045049463149…59552563980751850631

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

1.456 × 10¹⁰⁰(101-digit number)

14565722009009892629…19105127961503701259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.456 × 10¹⁰⁰(101-digit number)

14565722009009892629…19105127961503701261

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

2.913 × 10¹⁰⁰(101-digit number)

29131444018019785259…38210255923007402519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.913 × 10¹⁰⁰(101-digit number)

29131444018019785259…38210255923007402521

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

5.826 × 10¹⁰⁰(101-digit number)

58262888036039570519…76420511846014805039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.826 × 10¹⁰⁰(101-digit number)

58262888036039570519…76420511846014805041

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

1.165 × 10¹⁰¹(102-digit number)

11652577607207914103…52841023692029610079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.165 × 10¹⁰¹(102-digit number)

11652577607207914103…52841023692029610081

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