Block #239,318

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/2/2013, 12:53:02 AM · Difficulty 9.9542 · 6,550,600 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bba701a15c0eaab639c9d45aeb5139c47ddfc78078deae0ecf3a814a0a34802

View on Chainz ↗

Height

#239,318

Difficulty

9.954202

Transactions

Size

9.77 KB

Version

Bits

09f44695

Nonce

3,038

Timestamp

11/2/2013, 12:53:02 AM

Confirmations

6,550,600

Merkle Root

d662e24776a5d3b325fd52e1d747654dad132d3a28d9a82f3418eecfe927e867

Transactions (5)

Coinbasecf529c0d75cbcf…aeaae214a82fdf

1 in → 2 out10.2100 XPM137 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

bfc8449242bcfb…c64f4ad3c46c3b

50 in → 2 out200.0100 XPM7.23 KB

AbpSmE7h…e31QUQ92 AahGrnkx…xBWCEFD8

19ec9753a31fa6…4f32212f02062e

1 in → 1 out10.1100 XPM159 B

AMF6scky…ugQApVzx

8b3f94813dae56…7ddae91ae3e6dd

2 in → 1 out20.2000 XPM272 B

AMF6scky…ugQApVzx

368afaca020e50…4e1d471374d286

13 in → 2 out40.0103 XPM1.89 KB

AGmXQrYj…1BynLmXf AZiZ3BSK…ouABkYiL

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.

2.865 × 10⁹⁹(100-digit number)

28655859267157385814…43707361886931502079

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

2.865 × 10⁹⁹(100-digit number)

28655859267157385814…43707361886931502079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.865 × 10⁹⁹(100-digit number)

28655859267157385814…43707361886931502081

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

5.731 × 10⁹⁹(100-digit number)

57311718534314771628…87414723773863004159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.731 × 10⁹⁹(100-digit number)

57311718534314771628…87414723773863004161

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

1.146 × 10¹⁰⁰(101-digit number)

11462343706862954325…74829447547726008319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.146 × 10¹⁰⁰(101-digit number)

11462343706862954325…74829447547726008321

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

2.292 × 10¹⁰⁰(101-digit number)

22924687413725908651…49658895095452016639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.292 × 10¹⁰⁰(101-digit number)

22924687413725908651…49658895095452016641

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

4.584 × 10¹⁰⁰(101-digit number)

45849374827451817302…99317790190904033279

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