Block #507,212

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 2:18:11 PM · Difficulty 10.8159 · 6,309,754 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84ac86e7a17c703efd3c42aa614470bb4b846e40d7128bb4609fb83c99d98a25

View on Chainz ↗

Height

#507,212

Difficulty

10.815896

Transactions

Size

798 B

Version

Bits

0ad0de8e

Nonce

167,330

Timestamp

4/23/2014, 2:18:11 PM

Confirmations

6,309,754

Mined by

⛏️ LeAREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

ce82f29d868550109be32b6d4fc4d6d4666c12743d88d674ffe506367ce6f99c

Transactions (1)

Coinbasece82f29d868550…e506367ce6f99c

1 in → 19 out8.5300 XPM709 B

AREQGaCC…V47D9Shh AGz9gyZW…bo8NYQpw AUzEPJFG…kYkA5U9V AMW1p9oT…2TzdaZxH AbHY4iza…Yckt2J5W

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.

2.562 × 10⁹³(94-digit number)

25627720873364093571…52246327081377779199

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

2.562 × 10⁹³(94-digit number)

25627720873364093571…52246327081377779199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.562 × 10⁹³(94-digit number)

25627720873364093571…52246327081377779201

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

5.125 × 10⁹³(94-digit number)

51255441746728187143…04492654162755558399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.125 × 10⁹³(94-digit number)

51255441746728187143…04492654162755558401

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

1.025 × 10⁹⁴(95-digit number)

10251088349345637428…08985308325511116799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.025 × 10⁹⁴(95-digit number)

10251088349345637428…08985308325511116801

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

2.050 × 10⁹⁴(95-digit number)

20502176698691274857…17970616651022233599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.050 × 10⁹⁴(95-digit number)

20502176698691274857…17970616651022233601

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

4.100 × 10⁹⁴(95-digit number)

41004353397382549714…35941233302044467199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.100 × 10⁹⁴(95-digit number)

41004353397382549714…35941233302044467201

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 #507,212

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