Block #565,274

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/28/2014, 5:23:14 AM · Difficulty 10.9649 · 6,245,062 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c90f1aee6a01359117dc53eb2aff66f5e06ee08543efdb768276ad36a3976418

View on Chainz ↗

Height

#565,274

Difficulty

10.964937

Transactions

Size

733 B

Version

Bits

0af7061e

Nonce

63,502

Timestamp

5/28/2014, 5:23:14 AM

Confirmations

6,245,062

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

fff602a80244b111e64000567ea4264bf18f273d7d3e541f942934a683969b4b

Transactions (1)

Coinbasefff602a80244b1…2934a683969b4b

1 in → 17 out8.3000 XPM641 B

AGz9gyZW…bo8NYQpw AbPcCMg4…719q6mAX AXh3bnHa…j7qFoCbE AXVLciVJ…uTVo9CdN AUzEPJFG…kYkA5U9V

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.

2.593 × 10⁹⁹(100-digit number)

25932253796820649308…00238044336574419199

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

2.593 × 10⁹⁹(100-digit number)

25932253796820649308…00238044336574419199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.593 × 10⁹⁹(100-digit number)

25932253796820649308…00238044336574419201

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

5.186 × 10⁹⁹(100-digit number)

51864507593641298617…00476088673148838399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.186 × 10⁹⁹(100-digit number)

51864507593641298617…00476088673148838401

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

1.037 × 10¹⁰⁰(101-digit number)

10372901518728259723…00952177346297676799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.037 × 10¹⁰⁰(101-digit number)

10372901518728259723…00952177346297676801

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

2.074 × 10¹⁰⁰(101-digit number)

20745803037456519447…01904354692595353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.074 × 10¹⁰⁰(101-digit number)

20745803037456519447…01904354692595353601

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

4.149 × 10¹⁰⁰(101-digit number)

41491606074913038894…03808709385190707199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.149 × 10¹⁰⁰(101-digit number)

41491606074913038894…03808709385190707201

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 #565,274

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