Block #411,145

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 1:21:37 PM · Difficulty 10.4308 · 6,394,202 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae50d67d278e675a53da47dd905fa43c0cad851e90fede03f67e70042f586dd7

View on Chainz ↗

Height

#411,145

Difficulty

10.430843

Transactions

Size

846 B

Version

Bits

0a6e4bb4

Nonce

4,671

Timestamp

2/19/2014, 1:21:37 PM

Confirmations

6,394,202

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b10bd7c08dd93aee301381cfe6210570b58d5a8c3efbe0a78eb1161317b29600

Transactions (2)

Coinbase9dfa501a1630de…be22512735d7e2

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

b4f1ade5734b35…e63e389b272aa4

4 in → 1 out3.0843 XPM637 B

AG7EDEdQ…h97Hix8a

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.

6.602 × 10¹⁰⁰(101-digit number)

66022170943695841351…22078714978447882239

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

6.602 × 10¹⁰⁰(101-digit number)

66022170943695841351…22078714978447882239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.602 × 10¹⁰⁰(101-digit number)

66022170943695841351…22078714978447882241

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

1.320 × 10¹⁰¹(102-digit number)

13204434188739168270…44157429956895764479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.320 × 10¹⁰¹(102-digit number)

13204434188739168270…44157429956895764481

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

2.640 × 10¹⁰¹(102-digit number)

26408868377478336540…88314859913791528959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.640 × 10¹⁰¹(102-digit number)

26408868377478336540…88314859913791528961

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

5.281 × 10¹⁰¹(102-digit number)

52817736754956673081…76629719827583057919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.281 × 10¹⁰¹(102-digit number)

52817736754956673081…76629719827583057921

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

1.056 × 10¹⁰²(103-digit number)

10563547350991334616…53259439655166115839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.056 × 10¹⁰²(103-digit number)

10563547350991334616…53259439655166115841

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