Block #263,263

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 3:37:58 PM · Difficulty 9.9667 · 6,551,100 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a7134afd7112f9c1caf6b04abe39dbfa0e98aedfca2f81454c034f7056b37f73

View on Chainz ↗

Height

#263,263

Difficulty

9.966668

Transactions

Size

1.24 KB

Version

Bits

09f77786

Nonce

22,750

Timestamp

11/17/2013, 3:37:58 PM

Confirmations

6,551,100

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

d8f58602b9cd435fef8e39f351aef36325742a2f37357016323c606dec81934b

Transactions (3)

Coinbase6a1447136f97eb…a72b165927d7b7

1 in → 2 out10.0800 XPM137 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

0ca126c8617014…2b92fee8e1c2eb

1 in → 2 out186.4855 XPM225 B

ATPJeJbF…xhb5aCB3 AZdmkNt9…Dk8ffFeU

eee364f755878f…b6f44593af1126

5 in → 2 out74.2661 XPM816 B

AHcwo8wj…wUY2MyDg AcQ1JhAf…5juzjiY1

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.

1.902 × 10⁹⁴(95-digit number)

19026333801826642140…31096447312943739499

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

1.902 × 10⁹⁴(95-digit number)

19026333801826642140…31096447312943739499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.902 × 10⁹⁴(95-digit number)

19026333801826642140…31096447312943739501

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

3.805 × 10⁹⁴(95-digit number)

38052667603653284280…62192894625887478999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.805 × 10⁹⁴(95-digit number)

38052667603653284280…62192894625887479001

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

7.610 × 10⁹⁴(95-digit number)

76105335207306568561…24385789251774957999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.610 × 10⁹⁴(95-digit number)

76105335207306568561…24385789251774958001

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

1.522 × 10⁹⁵(96-digit number)

15221067041461313712…48771578503549915999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.522 × 10⁹⁵(96-digit number)

15221067041461313712…48771578503549916001

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

3.044 × 10⁹⁵(96-digit number)

30442134082922627424…97543157007099831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.044 × 10⁹⁵(96-digit number)

30442134082922627424…97543157007099832001

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 #263,263

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