Block #405,953

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 9:59:00 PM · Difficulty 10.4340 · 6,402,797 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e78e17d38f21f31caa23271b067a0b9d8f3dfee4bdb66fe4706c1967e50d463

View on Chainz ↗

Height

#405,953

Difficulty

10.434025

Transactions

Size

732 B

Version

Bits

0a6f1c3b

Nonce

7,123

Timestamp

2/15/2014, 9:59:00 PM

Confirmations

6,402,797

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

eae7a0f9db2b9199c7da036b6f38396b1c585328521a41ee149f76025c537c1e

Transactions (2)

Coinbase12bf4ef80752c5…f391cc7f89ae33

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

fea8d18810c5ed…9c52fbb4dafad9

3 in → 2 out8.9104 XPM523 B

AbKpjaZQ…zKNG9UTZ AeEFDbAk…Qf2gWWpR

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.

1.077 × 10¹⁰¹(102-digit number)

10771787152620922493…17747814981026623999

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

1.077 × 10¹⁰¹(102-digit number)

10771787152620922493…17747814981026623999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.077 × 10¹⁰¹(102-digit number)

10771787152620922493…17747814981026624001

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

2.154 × 10¹⁰¹(102-digit number)

21543574305241844987…35495629962053247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.154 × 10¹⁰¹(102-digit number)

21543574305241844987…35495629962053248001

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

4.308 × 10¹⁰¹(102-digit number)

43087148610483689975…70991259924106495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.308 × 10¹⁰¹(102-digit number)

43087148610483689975…70991259924106496001

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

8.617 × 10¹⁰¹(102-digit number)

86174297220967379951…41982519848212991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.617 × 10¹⁰¹(102-digit number)

86174297220967379951…41982519848212992001

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

1.723 × 10¹⁰²(103-digit number)

17234859444193475990…83965039696425983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.723 × 10¹⁰²(103-digit number)

17234859444193475990…83965039696425984001

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 #405,953

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