Block #510,980

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 11:16:00 PM · Difficulty 10.8284 · 6,315,335 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ad01845a46ba4db5ad95895acf680b0ac5737a3306cf4f7aba293f2a1ef860b

View on Chainz ↗

Height

#510,980

Difficulty

10.828374

Transactions

Size

2.10 KB

Version

Bits

0ad4104a

Nonce

262,010,714

Timestamp

4/25/2014, 11:16:00 PM

Confirmations

6,315,335

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f51fa9c99cd1926bff73f6c1ecad5341b09c06c387af23a112ad830d93062423

Transactions (5)

Coinbase9ebe973533fa36…28de37997fac37

1 in → 1 out8.5600 XPM116 B

AbwWkWZt…kawDhufa

9bcfd78ee831b5…e9203ade38a1b8

2 in → 2 out14.9100 XPM373 B

AZasRLps…qVSdTCis AKhTB8Pf…8KJEix1e

a81c2596cbc8bd…d78f09f45c3e4f

7 in → 2 out25.0185 XPM1.09 KB

AXxrVNcw…NCyxGL55 Ac3pbHye…mL2Ltd11

3f9a2bf14ac3dd…2ccdd50246cd03

1 in → 2 out7.4867 XPM226 B

AULkviz4…6ZwMzqc9 AWKRKeNA…NZGuX4i9

7dc63de58485f7…6b8b9a8f44ffa4

1 in → 2 out6.5043 XPM225 B

AG8u7ddV…cU5QJSqk ALntjzi3…5twYmgvu

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.

1.159 × 10⁹⁹(100-digit number)

11590377653961941787…93274414381326591999

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

1.159 × 10⁹⁹(100-digit number)

11590377653961941787…93274414381326591999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.159 × 10⁹⁹(100-digit number)

11590377653961941787…93274414381326592001

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

2.318 × 10⁹⁹(100-digit number)

23180755307923883575…86548828762653183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.318 × 10⁹⁹(100-digit number)

23180755307923883575…86548828762653184001

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

4.636 × 10⁹⁹(100-digit number)

46361510615847767150…73097657525306367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.636 × 10⁹⁹(100-digit number)

46361510615847767150…73097657525306368001

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

9.272 × 10⁹⁹(100-digit number)

92723021231695534300…46195315050612735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.272 × 10⁹⁹(100-digit number)

92723021231695534300…46195315050612736001

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

1.854 × 10¹⁰⁰(101-digit number)

18544604246339106860…92390630101225471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.854 × 10¹⁰⁰(101-digit number)

18544604246339106860…92390630101225472001

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 #510,980

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