Block #405,461

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 2:15:58 PM · Difficulty 10.4305 · 6,406,889 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6adf45fd5b3aa442095aa77e68f05dc7604abb13f15a4602875a467dd586faa8

View on Chainz ↗

Height

#405,461

Difficulty

10.430463

Transactions

Size

1.77 KB

Version

Bits

0a6e32d2

Nonce

12,927

Timestamp

2/15/2014, 2:15:58 PM

Confirmations

6,406,889

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

98097a0adc8bc0f60748e8fef20347e8f08dc983dd5a5d5e13adfd9508ac94b5

Transactions (3)

Coinbase93cc4667b590f8…ee28eacd7b0734

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

e65f658403c5b0…244e000a64c1c3

5 in → 15 out45.9600 XPM1.06 KB

AKU3ZWGP…dHtBKFTR AeKNrjNj…1NEq95Ta AU4rS8Uy…pkcv8QYw AGEE6Zjb…JEXkMfEx AFqwEJFf…zqg3ZgE6

14ef4a6c76457a…4f46241ce17a0c

3 in → 2 out11.0106 XPM524 B

AHTzTeFx…otr7JtM6 AXazPKor…Tphices5

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.

8.401 × 10⁹⁴(95-digit number)

84011722815698773559…30672167208824371179

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

8.401 × 10⁹⁴(95-digit number)

84011722815698773559…30672167208824371179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.401 × 10⁹⁴(95-digit number)

84011722815698773559…30672167208824371181

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

1.680 × 10⁹⁵(96-digit number)

16802344563139754711…61344334417648742359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.680 × 10⁹⁵(96-digit number)

16802344563139754711…61344334417648742361

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

3.360 × 10⁹⁵(96-digit number)

33604689126279509423…22688668835297484719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.360 × 10⁹⁵(96-digit number)

33604689126279509423…22688668835297484721

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

6.720 × 10⁹⁵(96-digit number)

67209378252559018847…45377337670594969439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.720 × 10⁹⁵(96-digit number)

67209378252559018847…45377337670594969441

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

1.344 × 10⁹⁶(97-digit number)

13441875650511803769…90754675341189938879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.344 × 10⁹⁶(97-digit number)

13441875650511803769…90754675341189938881

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 #405,461

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