Block #288,194

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 3:27:08 PM · Difficulty 9.9875 · 6,515,726 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75dbf70bce1e9e72dc19a26e218f369a11f5b56cbcd42c04311602f24421ca69

View on Chainz ↗

Height

#288,194

Difficulty

9.987473

Transactions

Size

1.03 KB

Version

Bits

09fccb0e

Nonce

17,435

Timestamp

12/1/2013, 3:27:08 PM

Confirmations

6,515,726

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

abed99066a045ddb7ea9da721add5ea548d2c03626b02cf5e4e253cdf08197ba

Transactions (2)

Coinbase0c03533642ab90…77ceb36c44e64c

1 in → 2 out10.0200 XPM140 B

AYaTpnoD…EJq25nUy AKNbfPoc…jfkpwAyL

1a0295c2946669…54237abd0da5f8

5 in → 2 out1.3148 XPM818 B

AWALDFQX…HbW326xX ALabxQbo…2JbrwVRJ

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.

2.863 × 10¹⁰¹(102-digit number)

28635575981368078647…70357816294191257599

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

2.863 × 10¹⁰¹(102-digit number)

28635575981368078647…70357816294191257599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.863 × 10¹⁰¹(102-digit number)

28635575981368078647…70357816294191257601

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

5.727 × 10¹⁰¹(102-digit number)

57271151962736157295…40715632588382515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.727 × 10¹⁰¹(102-digit number)

57271151962736157295…40715632588382515201

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

1.145 × 10¹⁰²(103-digit number)

11454230392547231459…81431265176765030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.145 × 10¹⁰²(103-digit number)

11454230392547231459…81431265176765030401

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

2.290 × 10¹⁰²(103-digit number)

22908460785094462918…62862530353530060799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.290 × 10¹⁰²(103-digit number)

22908460785094462918…62862530353530060801

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

4.581 × 10¹⁰²(103-digit number)

45816921570188925836…25725060707060121599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.581 × 10¹⁰²(103-digit number)

45816921570188925836…25725060707060121601

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