Block #478,196

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 10:30:55 PM · Difficulty 10.4911 · 6,316,114 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9027546768449b46aef8c9ad1a23daa4d51df5a30cba8c7330ff34935b954ca8

View on Chainz ↗

Height

#478,196

Difficulty

10.491094

Transactions

Size

901 B

Version

Bits

0a7db84e

Nonce

204,579

Timestamp

4/6/2014, 10:30:55 PM

Confirmations

6,316,114

Merkle Root

e7175c79dffe32008095f7dd228a23d52157f3e2b1a50cf2305f353de3104e33

Transactions (1)

Coinbasee7175c79dffe32…5f353de3104e33

1 in → 22 out9.0700 XPM811 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

2.421 × 10⁹⁵(96-digit number)

24216650913879739084…35479990766001971199

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

2.421 × 10⁹⁵(96-digit number)

24216650913879739084…35479990766001971199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.421 × 10⁹⁵(96-digit number)

24216650913879739084…35479990766001971201

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

4.843 × 10⁹⁵(96-digit number)

48433301827759478168…70959981532003942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.843 × 10⁹⁵(96-digit number)

48433301827759478168…70959981532003942401

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

9.686 × 10⁹⁵(96-digit number)

96866603655518956336…41919963064007884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.686 × 10⁹⁵(96-digit number)

96866603655518956336…41919963064007884801

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

1.937 × 10⁹⁶(97-digit number)

19373320731103791267…83839926128015769599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.937 × 10⁹⁶(97-digit number)

19373320731103791267…83839926128015769601

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

3.874 × 10⁹⁶(97-digit number)

38746641462207582534…67679852256031539199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.874 × 10⁹⁶(97-digit number)

38746641462207582534…67679852256031539201

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