Block #419,134

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 9:29:04 AM · Difficulty 10.3857 · 6,380,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

209b637d3f0d7b25e552ac439c50091e6a703af8288e848e57e51ab41096d31a

View on Chainz ↗

Height

#419,134

Difficulty

10.385714

Transactions

Size

1.58 KB

Version

Bits

0a62be29

Nonce

36,578

Timestamp

2/25/2014, 9:29:04 AM

Confirmations

6,380,221

Mined by

⛏️ >eaSbALqxX1WA4yGGdvvcw46Ggu5ZRhhsKjbnXn

Merkle Root

b8d168db094099b181c137c21704621ed03775b4fca80765252690d885465ec2

Transactions (4)

Coinbase7c4c240c155e81…e456182c7bbead

1 in → 23 out9.2600 XPM845 B

ALqxX1WA…hsKjbnXn ALekigZz…VuGVXmbb Ad92dXD3…NucMrh77 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6

2d83c44f37a2ab…54c15b7d75f4f3

1 in → 2 out8.1748 XPM225 B

AdSjszHw…mmrvZrWy AGTNEB7S…PFVAcfDh

2ea3121d255b4e…41b3f4924310b6

1 in → 2 out8.1724 XPM226 B

AdbyvYKY…RWaHUgb6 AeW1rttf…s9QpwuSL

bb77078e92b692…d137adf13afb8d

1 in → 2 out8.1686 XPM226 B

AVBYQUMF…igi87Tx4 AXhWtbPt…5LyuGMVA

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.

7.149 × 10¹⁰⁰(101-digit number)

71496005082843426075…04744517638667883519

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

7.149 × 10¹⁰⁰(101-digit number)

71496005082843426075…04744517638667883519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.149 × 10¹⁰⁰(101-digit number)

71496005082843426075…04744517638667883521

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

1.429 × 10¹⁰¹(102-digit number)

14299201016568685215…09489035277335767039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.429 × 10¹⁰¹(102-digit number)

14299201016568685215…09489035277335767041

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

2.859 × 10¹⁰¹(102-digit number)

28598402033137370430…18978070554671534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.859 × 10¹⁰¹(102-digit number)

28598402033137370430…18978070554671534081

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

5.719 × 10¹⁰¹(102-digit number)

57196804066274740860…37956141109343068159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.719 × 10¹⁰¹(102-digit number)

57196804066274740860…37956141109343068161

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

1.143 × 10¹⁰²(103-digit number)

11439360813254948172…75912282218686136319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.143 × 10¹⁰²(103-digit number)

11439360813254948172…75912282218686136321

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