Block #290,525

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 5:53:25 PM · Difficulty 9.9893 · 6,503,812 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40d7bc2289b90c1b82215b8997cf2a63ca70985b379850178c0ea97caca65826

View on Chainz ↗

Height

#290,525

Difficulty

9.989261

Transactions

Size

970 B

Version

Bits

09fd403d

Nonce

66,298

Timestamp

12/2/2013, 5:53:25 PM

Confirmations

6,503,812

Merkle Root

a02fd50aa8288ba1c9a3f226ba3b0f27454f7298b5c36baff2b3ce6846e9526c

Transactions (1)

Coinbasea02fd50aa8288b…b3ce6846e9526c

1 in → 24 out10.0098 XPM879 B

AZninDSu…FvgDMwC4 AWXYBWKP…qQAoisBJ AQwRN8bE…V8PsTcY9 AYcLTeXR…bscgPops AVss9H5F…zXhyMijY

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.

6.184 × 10⁹⁶(97-digit number)

61843787976838021923…25452576305165111029

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

6.184 × 10⁹⁶(97-digit number)

61843787976838021923…25452576305165111029

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.184 × 10⁹⁶(97-digit number)

61843787976838021923…25452576305165111031

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

1.236 × 10⁹⁷(98-digit number)

12368757595367604384…50905152610330222059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.236 × 10⁹⁷(98-digit number)

12368757595367604384…50905152610330222061

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

2.473 × 10⁹⁷(98-digit number)

24737515190735208769…01810305220660444119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.473 × 10⁹⁷(98-digit number)

24737515190735208769…01810305220660444121

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

4.947 × 10⁹⁷(98-digit number)

49475030381470417538…03620610441320888239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.947 × 10⁹⁷(98-digit number)

49475030381470417538…03620610441320888241

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

9.895 × 10⁹⁷(98-digit number)

98950060762940835077…07241220882641776479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.895 × 10⁹⁷(98-digit number)

98950060762940835077…07241220882641776481

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