Block #466,512

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 5:40:21 AM · Difficulty 10.4215 · 6,367,382 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a14dd2415ca8e99622b74e73fb1352082b011949d80db361da77006b38c81028

View on Chainz ↗

Height

#466,512

Difficulty

10.421507

Transactions

Size

209 B

Version

Bits

0a6be7dd

Nonce

8,802

Timestamp

3/30/2014, 5:40:21 AM

Confirmations

6,367,382

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d41101febf8b63d1c66443c4c66c503742f4549b0328efb4eac3193bf3d07a69

Transactions (1)

Coinbased41101febf8b63…c3193bf3d07a69

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

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.

4.127 × 10¹⁰²(103-digit number)

41271148423392805041…85153149954686975999

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

4.127 × 10¹⁰²(103-digit number)

41271148423392805041…85153149954686975999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.127 × 10¹⁰²(103-digit number)

41271148423392805041…85153149954686976001

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

8.254 × 10¹⁰²(103-digit number)

82542296846785610083…70306299909373951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.254 × 10¹⁰²(103-digit number)

82542296846785610083…70306299909373952001

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

1.650 × 10¹⁰³(104-digit number)

16508459369357122016…40612599818747903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.650 × 10¹⁰³(104-digit number)

16508459369357122016…40612599818747904001

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

3.301 × 10¹⁰³(104-digit number)

33016918738714244033…81225199637495807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.301 × 10¹⁰³(104-digit number)

33016918738714244033…81225199637495808001

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

6.603 × 10¹⁰³(104-digit number)

66033837477428488066…62450399274991615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.603 × 10¹⁰³(104-digit number)

66033837477428488066…62450399274991616001

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 #466,512

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