Block #243,577

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 9:19:56 AM · Difficulty 9.9617 · 6,567,008 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

705846b783cd024e9b18fa2b24336c14bd861c48b96629614e68f8b114850a07

View on Chainz ↗

Height

#243,577

Difficulty

9.961651

Transactions

Size

909 B

Version

Bits

09f62ec4

Nonce

12,441

Timestamp

11/4/2013, 9:19:56 AM

Confirmations

6,567,008

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

528952eee29f4d04077e312c62f2e2f77c6fc51cc96f9f5c36298c17a350c1cd

Transactions (4)

Coinbasea4aacd4f946c4e…09bf1ce6002aed

1 in → 2 out10.0900 XPM136 B

AZDUEbdS…RYKMRZET Abiw8n3q…ZnZfgvQW

3bd2be9f7628a5…e9c713562aae44

1 in → 2 out10.0600 XPM226 B

APovXhSy…SxuJqUMB AYAMdyqn…i4JU6pMg

0f7f55e7e6d248…300a802c5198d3

1 in → 2 out7.9735 XPM227 B

AHweeAja…eoeYixaL AGvZvGD7…mfeP2xnr

e85b08f0af5235…bc4830d893f545

1 in → 2 out4.0041 XPM227 B

AM7kr9r8…eopw6ER5 ATqDht7F…xHD53DYv

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.

2.008 × 10¹⁰¹(102-digit number)

20081876519121068468…02931924437847516159

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

2.008 × 10¹⁰¹(102-digit number)

20081876519121068468…02931924437847516159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.008 × 10¹⁰¹(102-digit number)

20081876519121068468…02931924437847516161

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

4.016 × 10¹⁰¹(102-digit number)

40163753038242136936…05863848875695032319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.016 × 10¹⁰¹(102-digit number)

40163753038242136936…05863848875695032321

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

8.032 × 10¹⁰¹(102-digit number)

80327506076484273873…11727697751390064639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.032 × 10¹⁰¹(102-digit number)

80327506076484273873…11727697751390064641

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

1.606 × 10¹⁰²(103-digit number)

16065501215296854774…23455395502780129279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.606 × 10¹⁰²(103-digit number)

16065501215296854774…23455395502780129281

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

3.213 × 10¹⁰²(103-digit number)

32131002430593709549…46910791005560258559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.213 × 10¹⁰²(103-digit number)

32131002430593709549…46910791005560258561

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 #243,577

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