Block #289,916

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 10:39:22 AM · Difficulty 9.9889 · 6,521,136 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27e16d14d5979fb5b17830d5853d342fba58d041cbd7deb1a8a0149da4405964

View on Chainz ↗

Height

#289,916

Difficulty

9.988869

Transactions

Size

969 B

Version

Bits

09fd2680

Nonce

8,552

Timestamp

12/2/2013, 10:39:22 AM

Confirmations

6,521,136

Mined by

⛏️ |laRcqAc5sZcdPRNjfrTK9pchLQrJN4XkzV4eckG

Merkle Root

87951d7737046c170494ce423865c51d982132ddc06e1728a6714ec87277c211

Transactions (1)

Coinbase87951d7737046c…714ec87277c211

1 in → 24 out10.0061 XPM879 B

Ac5sZcdP…kzV4eckG AKEwr54i…9BfmMkRh Ae58nAEb…GFUA15fv AZ3bZpff…LnRQBGfh AbUZ8W5N…wEAzXuVd

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.

1.225 × 10⁹⁴(95-digit number)

12255200923527503417…46264174621774905599

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

1.225 × 10⁹⁴(95-digit number)

12255200923527503417…46264174621774905599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.225 × 10⁹⁴(95-digit number)

12255200923527503417…46264174621774905601

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

2.451 × 10⁹⁴(95-digit number)

24510401847055006834…92528349243549811199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.451 × 10⁹⁴(95-digit number)

24510401847055006834…92528349243549811201

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

4.902 × 10⁹⁴(95-digit number)

49020803694110013669…85056698487099622399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.902 × 10⁹⁴(95-digit number)

49020803694110013669…85056698487099622401

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

9.804 × 10⁹⁴(95-digit number)

98041607388220027338…70113396974199244799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.804 × 10⁹⁴(95-digit number)

98041607388220027338…70113396974199244801

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

1.960 × 10⁹⁵(96-digit number)

19608321477644005467…40226793948398489599

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 #289,916

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