Block #1,305,430

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/30/2015, 7:01:59 PM · Difficulty 10.8502 · 5,502,912 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abf40f876f24736e9c1cc727682e94ed7b44aded8bf16c704028237df98e35d2

View on Chainz ↗

Height

#1,305,430

Difficulty

10.850162

Transactions

Size

4.62 KB

Version

Bits

0ad9a43a

Nonce

104,814,220

Timestamp

10/30/2015, 7:01:59 PM

Confirmations

5,502,912

Mined by

⛏️ P2SHAP8ANRRFHJLPW3dF5gCbfjXHND6wQjmiyJ

Merkle Root

e8d724059c2f4fde83c1e10c31e958af7b6bbf2244238af55d647c40ef47b929

Transactions (4)

Coinbasea30a45caac3a2d…ddb3e56d71f362

1 in → 1 out8.5400 XPM109 B

AP8ANRRF…6wQjmiyJ

ebed743a686191…ea30ed529e7224

1 in → 51 out4.8876 XPM1.85 KB

AHdcBgRC…QMQBUujf AdYGfqwk…ZfcDBb3D AdyZPRdu…hfYWPqW3 AKpQDAmz…vQzXuVyw AJ5u3Hok…zj9uSzXD

c147539609e0f8…da7034133612b6

1 in → 13 out48.1210 XPM600 B

AYopH4gS…huNmLdsn AdAQ18BM…AZe97t1s AJ9cg1cG…6caZy7Ld ARJYHjqb…YTEy5rEj AG97kpGV…BGGHr9WA

eb54acc63821bf…0f46c21637bb51

2 in → 51 out1.2161 XPM1.99 KB

AGwbxzZC…qRzQdmue AMacMCey…6BWVpoaM AS7EhQy8…svFmz7yp ATqg91dJ…4TDfzWjY AKqpP3is…La18Rtr4

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.

1.584 × 10⁹⁶(97-digit number)

15840172447505888041…33822115951754588159

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

1.584 × 10⁹⁶(97-digit number)

15840172447505888041…33822115951754588159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.584 × 10⁹⁶(97-digit number)

15840172447505888041…33822115951754588161

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

3.168 × 10⁹⁶(97-digit number)

31680344895011776082…67644231903509176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.168 × 10⁹⁶(97-digit number)

31680344895011776082…67644231903509176321

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

6.336 × 10⁹⁶(97-digit number)

63360689790023552165…35288463807018352639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.336 × 10⁹⁶(97-digit number)

63360689790023552165…35288463807018352641

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

1.267 × 10⁹⁷(98-digit number)

12672137958004710433…70576927614036705279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.267 × 10⁹⁷(98-digit number)

12672137958004710433…70576927614036705281

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

2.534 × 10⁹⁷(98-digit number)

25344275916009420866…41153855228073410559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.534 × 10⁹⁷(98-digit number)

25344275916009420866…41153855228073410561

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 #1,305,430

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