Block #408,586

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/17/2014, 6:31:36 PM · Difficulty 10.4306 · 6,416,779 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fbef2c9b9b0e3138b79eb7f48763ad372e36c6cf323301da933c134ef9625f45

View on Chainz ↗

Height

#408,586

Difficulty

10.430626

Transactions

Size

2.05 KB

Version

Bits

0a6e3d83

Nonce

32,895

Timestamp

2/17/2014, 6:31:36 PM

Confirmations

6,416,779

Mined by

⛏️ <aSUJAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1c191b20eb22b53b45985650bd7b93b0fe29fa81268d41ac39121adef01d65d7

Transactions (4)

Coinbase78481f46c3dd86…92f3227ae1a793

1 in → 20 out9.1800 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AP5UvYhU…vLTDwkdA AT6V8ebA…kxfTNYPW AGKhfQo2…h7fBXLX6

9240ba3751ae8f…dcf6cab375db6c

3 in → 2 out25.5306 XPM521 B

AW9RX6er…MSXGpPNt AXfZxKeP…Q3pkDmTS

f08a0eeb22b0d7…40f25e38bb662d

3 in → 2 out1.0955 XPM522 B

AXnL68UR…jsxeGUhN AN1eq4Yf…pQiADVGN

f2f1785d55efba…5af8aa039a136b

1 in → 2 out1.0653 XPM225 B

ARd47WCo…vXzjgLiX AJVeqnSy…PSXL1grX

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.

1.571 × 10⁹²(93-digit number)

15714367250363284161…96531443581902200879

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

1.571 × 10⁹²(93-digit number)

15714367250363284161…96531443581902200879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.571 × 10⁹²(93-digit number)

15714367250363284161…96531443581902200881

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

3.142 × 10⁹²(93-digit number)

31428734500726568323…93062887163804401759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.142 × 10⁹²(93-digit number)

31428734500726568323…93062887163804401761

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

6.285 × 10⁹²(93-digit number)

62857469001453136647…86125774327608803519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.285 × 10⁹²(93-digit number)

62857469001453136647…86125774327608803521

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

1.257 × 10⁹³(94-digit number)

12571493800290627329…72251548655217607039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.257 × 10⁹³(94-digit number)

12571493800290627329…72251548655217607041

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

2.514 × 10⁹³(94-digit number)

25142987600581254658…44503097310435214079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.514 × 10⁹³(94-digit number)

25142987600581254658…44503097310435214081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.028 × 10⁹³(94-digit number)

50285975201162509317…89006194620870428159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #408,586

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