Block #435,163

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/8/2014, 5:37:17 PM · Difficulty 10.3561 · 6,370,894 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3ef79337cbc02865e3f9049a719eeaaa5c353595868ade0d2324255eab97b81

View on Chainz ↗

Height

#435,163

Difficulty

10.356103

Transactions

Size

34.26 KB

Version

Bits

0a5b2990

Nonce

6,825

Timestamp

3/8/2014, 5:37:17 PM

Confirmations

6,370,894

Mined by

⛏️ aSUE<AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c8c7965919d1d34275c65ff8014adb852f0fad4c227e77cbf0052682db177909

Transactions (2)

Coinbasef196ec687af1f1…1545a4381b1e93

1 in → 24 out9.3100 XPM879 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

5267f67a399d87…a6a85177624cda

230 in → 2 out77.6942 XPM33.31 KB

AK7VLLhp…dicvcQRU AY1mxbcD…PbgbDXGe

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.

2.356 × 10⁹⁶(97-digit number)

23566316958965321628…87934283371862273599

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

2.356 × 10⁹⁶(97-digit number)

23566316958965321628…87934283371862273599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.356 × 10⁹⁶(97-digit number)

23566316958965321628…87934283371862273601

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

4.713 × 10⁹⁶(97-digit number)

47132633917930643256…75868566743724547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.713 × 10⁹⁶(97-digit number)

47132633917930643256…75868566743724547201

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

9.426 × 10⁹⁶(97-digit number)

94265267835861286513…51737133487449094399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.426 × 10⁹⁶(97-digit number)

94265267835861286513…51737133487449094401

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

1.885 × 10⁹⁷(98-digit number)

18853053567172257302…03474266974898188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.885 × 10⁹⁷(98-digit number)

18853053567172257302…03474266974898188801

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

3.770 × 10⁹⁷(98-digit number)

37706107134344514605…06948533949796377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.770 × 10⁹⁷(98-digit number)

37706107134344514605…06948533949796377601

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