Block #423,581

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 1:07:01 PM · Difficulty 10.3759 · 6,384,161 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d8dc56bcb62f64353c62d6ec0ed1367b1b0e774e724a2e5e3cf9c15acc71e5c

View on Chainz ↗

Height

#423,581

Difficulty

10.375852

Transactions

Size

1.49 KB

Version

Bits

0a6037ce

Nonce

26,754

Timestamp

2/28/2014, 1:07:01 PM

Confirmations

6,384,161

Mined by

⛏️ vaSAGD4yZQwygGFSCiBcSnuDhf75LhGzM2XAx

Merkle Root

920683764cebc38918c1b1ebf050921218989872ea1e4522711519e7439329eb

Transactions (2)

Coinbasea1eeeb71b6895e…316043e368b1b8

1 in → 26 out9.2700 XPM947 B

AGD4yZQw…hGzM2XAx AZemWJAo…6jhDtieG AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

84621510c3b289…597006280490c1

3 in → 1 out358.0000 XPM488 B

ASQvCg4A…hQn3kS8p

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.

6.283 × 10⁹⁵(96-digit number)

62837059312923128316…79208854779745126399

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

6.283 × 10⁹⁵(96-digit number)

62837059312923128316…79208854779745126399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.283 × 10⁹⁵(96-digit number)

62837059312923128316…79208854779745126401

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

1.256 × 10⁹⁶(97-digit number)

12567411862584625663…58417709559490252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.256 × 10⁹⁶(97-digit number)

12567411862584625663…58417709559490252801

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

2.513 × 10⁹⁶(97-digit number)

25134823725169251326…16835419118980505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.513 × 10⁹⁶(97-digit number)

25134823725169251326…16835419118980505601

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

5.026 × 10⁹⁶(97-digit number)

50269647450338502653…33670838237961011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.026 × 10⁹⁶(97-digit number)

50269647450338502653…33670838237961011201

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

1.005 × 10⁹⁷(98-digit number)

10053929490067700530…67341676475922022399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.005 × 10⁹⁷(98-digit number)

10053929490067700530…67341676475922022401

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 #423,581

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