Block #286,619

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 11:30:24 PM · Difficulty 9.9858 · 6,540,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5679371cec05cdd58c3252598f4f61b402572ef2cbecc9597b06dd2ebe66ca17

View on Chainz ↗

Height

#286,619

Difficulty

9.985787

Transactions

Size

908 B

Version

Bits

09fc5c84

Nonce

41,624

Timestamp

11/30/2013, 11:30:24 PM

Confirmations

6,540,326

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bd92fd0175f057f0d41e1ce8fb7fb45a373f2463a1fccc625dc2c8c381a3b8c0

Transactions (2)

Coinbasea8a180a2df1f7d…0172d60e39f042

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

58cb9aa3d06fa0…338d905c7812a7

4 in → 3 out213.9196 XPM707 B

ANarSico…DtDpaqWz ATGKWk5X…NYUFwTVg AKL54C6b…jiNwJAtX

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.

9.815 × 10⁹⁵(96-digit number)

98152094316331317669…91132976518823707999

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

9.815 × 10⁹⁵(96-digit number)

98152094316331317669…91132976518823707999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.815 × 10⁹⁵(96-digit number)

98152094316331317669…91132976518823708001

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

1.963 × 10⁹⁶(97-digit number)

19630418863266263533…82265953037647415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.963 × 10⁹⁶(97-digit number)

19630418863266263533…82265953037647416001

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

3.926 × 10⁹⁶(97-digit number)

39260837726532527067…64531906075294831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.926 × 10⁹⁶(97-digit number)

39260837726532527067…64531906075294832001

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

7.852 × 10⁹⁶(97-digit number)

78521675453065054135…29063812150589663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.852 × 10⁹⁶(97-digit number)

78521675453065054135…29063812150589664001

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

1.570 × 10⁹⁷(98-digit number)

15704335090613010827…58127624301179327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.570 × 10⁹⁷(98-digit number)

15704335090613010827…58127624301179328001

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

Block #286,619

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