Block #411,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 9:49:47 PM · Difficulty 10.4244 · 6,403,215 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1105d3d8544267d3ac6c086f58b41990750e4ba4a02a5f65e6335e9902b29ed2

View on Chainz ↗

Height

#411,595

Difficulty

10.424387

Transactions

Size

1.36 KB

Version

Bits

0a6ca4a5

Nonce

479,865

Timestamp

2/19/2014, 9:49:47 PM

Confirmations

6,403,215

Mined by

⛏️ P2SHAKmPthuDcpE17F3KbmaGdC42yLRbrkDjoJ

Merkle Root

4f34ae6fec4335de7625ee4dd1ecd411df9b7d2f812a1822529ae3357b2ffaba

Transactions (3)

Coinbase3017ebda443d22…07ab1f83c4c86e

1 in → 1 out9.2100 XPM109 B

AKmPthuD…RbrkDjoJ

04395899920fbc…c27469f08385de

3 in → 2 out264.4700 XPM520 B

Ac9vBEsi…zucYArPa AY6X9F54…JPuCTR4D

ac355a5b13dc25…e1796ba07cb36f

4 in → 2 out12.1315 XPM670 B

AMabBUHL…QmGYxwpC AaL9gVGX…ALi5XVip

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.

4.021 × 10⁹³(94-digit number)

40213464971515969398…45984041240058056999

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

4.021 × 10⁹³(94-digit number)

40213464971515969398…45984041240058056999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.021 × 10⁹³(94-digit number)

40213464971515969398…45984041240058057001

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

8.042 × 10⁹³(94-digit number)

80426929943031938796…91968082480116113999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.042 × 10⁹³(94-digit number)

80426929943031938796…91968082480116114001

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

1.608 × 10⁹⁴(95-digit number)

16085385988606387759…83936164960232227999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.608 × 10⁹⁴(95-digit number)

16085385988606387759…83936164960232228001

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

3.217 × 10⁹⁴(95-digit number)

32170771977212775518…67872329920464455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.217 × 10⁹⁴(95-digit number)

32170771977212775518…67872329920464456001

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

6.434 × 10⁹⁴(95-digit number)

64341543954425551036…35744659840928911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.434 × 10⁹⁴(95-digit number)

64341543954425551036…35744659840928912001

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 #411,595

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