Block #244,043

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 3:26:53 PM · Difficulty 9.9624 · 6,564,298 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed02c549e83cff95aa524379ef4503f3bb15883ada6e70eeebbdc0a35698dc5b

View on Chainz ↗

Height

#244,043

Difficulty

9.962412

Transactions

Size

977 B

Version

Bits

09f660a8

Nonce

1,615

Timestamp

11/4/2013, 3:26:53 PM

Confirmations

6,564,298

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

f3807707fb452fbed118f19739f40fc5528d3932493a1f9540c4a6ec961ddd65

Transactions (3)

Coinbase49edd5b9d1afa7…cbd95d985dcc12

1 in → 2 out10.0800 XPM137 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

96297df0c4f71c…f50986c2a62705

1 in → 2 out8.0470 XPM227 B

AeEkBdgQ…cT5B1JfR AY1ZK2KH…EFd4Jne1

f02f347474ed24…abee951712849b

3 in → 2 out3.4619 XPM520 B

AL6HxL8i…635ScZR6 AZMxFgaw…QaMdG3Ce

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.

7.879 × 10¹⁰¹(102-digit number)

78798515015209329373…69174536804493644799

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

7.879 × 10¹⁰¹(102-digit number)

78798515015209329373…69174536804493644799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.879 × 10¹⁰¹(102-digit number)

78798515015209329373…69174536804493644801

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

1.575 × 10¹⁰²(103-digit number)

15759703003041865874…38349073608987289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.575 × 10¹⁰²(103-digit number)

15759703003041865874…38349073608987289601

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

3.151 × 10¹⁰²(103-digit number)

31519406006083731749…76698147217974579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.151 × 10¹⁰²(103-digit number)

31519406006083731749…76698147217974579201

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

6.303 × 10¹⁰²(103-digit number)

63038812012167463498…53396294435949158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.303 × 10¹⁰²(103-digit number)

63038812012167463498…53396294435949158401

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

1.260 × 10¹⁰³(104-digit number)

12607762402433492699…06792588871898316799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #244,043

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