Block #406,062

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 11:45:32 PM · Difficulty 10.4347 · 6,399,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d51ea0c23ab9749d912f0343f7c7ffa7da7ae9e0879d7baea154d8de9e6b43fc

View on Chainz ↗

Height

#406,062

Difficulty

10.434726

Transactions

Size

1.80 KB

Version

Bits

0a6f4a34

Nonce

138,742

Timestamp

2/15/2014, 11:45:32 PM

Confirmations

6,399,728

Mined by

⛏️ .2_xAMW1p9oTkBzM1hi3okaKfJzfWi2TzdaZxH

Merkle Root

42866f7f3a9a346a531ac39be69e50ea657df9b51741ac64bc387886ad7d1dea

Transactions (2)

Coinbase1f188083e7e3b1…daeae393732b17

1 in → 22 out9.1900 XPM811 B

AMW1p9oT…2TzdaZxH AZuKpVkB…HFoeLG6t AZqjMFvv…G8aw2zC8 ATp4jJhs…TbSgR8Qb AczyTBWn…bEQQj33u

bb58062930d593…70c4147fe0d559

4 in → 11 out10.9824 XPM941 B

AJ7bwxHw…vy276KPV ALWzM1NK…XM7hzshS ANPtbNPi…RBKxFzhV AKZqAaBK…4jDn8ef3 APPZLZRh…k8wT1gVi

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.

1.901 × 10⁹⁹(100-digit number)

19011118588642314770…84580706007210444799

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

1.901 × 10⁹⁹(100-digit number)

19011118588642314770…84580706007210444799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.901 × 10⁹⁹(100-digit number)

19011118588642314770…84580706007210444801

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

3.802 × 10⁹⁹(100-digit number)

38022237177284629540…69161412014420889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.802 × 10⁹⁹(100-digit number)

38022237177284629540…69161412014420889601

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

7.604 × 10⁹⁹(100-digit number)

76044474354569259080…38322824028841779199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.604 × 10⁹⁹(100-digit number)

76044474354569259080…38322824028841779201

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

1.520 × 10¹⁰⁰(101-digit number)

15208894870913851816…76645648057683558399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.520 × 10¹⁰⁰(101-digit number)

15208894870913851816…76645648057683558401

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

3.041 × 10¹⁰⁰(101-digit number)

30417789741827703632…53291296115367116799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.041 × 10¹⁰⁰(101-digit number)

30417789741827703632…53291296115367116801

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