Block #396,020

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 3:28:17 AM · Difficulty 10.4092 · 6,405,793 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9e305e86217f713f8c9173af5321ca28fcd802b763ca966139826ebdbe9dd81

View on Chainz ↗

Height

#396,020

Difficulty

10.409224

Transactions

Size

1.08 KB

Version

Bits

0a68c2e8

Nonce

1,070

Timestamp

2/9/2014, 3:28:17 AM

Confirmations

6,405,793

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a11422b74a636e37c0d2e7a0ceff9fcd6a95fcd04ff2fc0f1f148db5de7b75f8

Transactions (3)

Coinbase8c9d6fc702ed33…cf5c17e16dca4c

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

eff011c3519271…9e3650bcd67e98

3 in → 2 out0.8398 XPM524 B

AcWn2fxt…ibzMfEDX AZvN5eQp…hLZKTumb

c00776e9a077bc…dc4630b6afa098

2 in → 2 out3.3076 XPM373 B

Ac3zha6j…BW4cX7US ARu9VUSb…HijDSGGv

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.

3.006 × 10¹⁰²(103-digit number)

30063930314101004219…52047625118723112959

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

3.006 × 10¹⁰²(103-digit number)

30063930314101004219…52047625118723112959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.006 × 10¹⁰²(103-digit number)

30063930314101004219…52047625118723112961

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

6.012 × 10¹⁰²(103-digit number)

60127860628202008438…04095250237446225919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.012 × 10¹⁰²(103-digit number)

60127860628202008438…04095250237446225921

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

1.202 × 10¹⁰³(104-digit number)

12025572125640401687…08190500474892451839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.202 × 10¹⁰³(104-digit number)

12025572125640401687…08190500474892451841

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

2.405 × 10¹⁰³(104-digit number)

24051144251280803375…16381000949784903679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.405 × 10¹⁰³(104-digit number)

24051144251280803375…16381000949784903681

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

4.810 × 10¹⁰³(104-digit number)

48102288502561606751…32762001899569807359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.810 × 10¹⁰³(104-digit number)

48102288502561606751…32762001899569807361

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