Block #2,267,345

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2017, 1:12:04 PM · Difficulty 10.9517 · 4,566,481 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c83dee1deebe2e6476f8f6b677804127cba96821d0d61e898e0a4d6e7b423fd9

View on Chainz ↗

Height

#2,267,345

Difficulty

10.951715

Transactions

Size

721 B

Version

Bits

0af3a394

Nonce

263,964,205

Timestamp

8/25/2017, 1:12:04 PM

Confirmations

4,566,481

Mined by

⛏️ P2SHAMj8eXThoPhnvZYpPXwzvBo2LRiMFzgFh9

Merkle Root

e854956af7eeddb8fdb9aa7c1575d68aaa8d0f20a6907982f25137f28f061698

Transactions (2)

Coinbasea6003ff30d70d3…41e921952c6cf5

1 in → 1 out8.3300 XPM109 B

AMj8eXTh…iMFzgFh9

1c823978976eaa…a0adae921cf279

3 in → 2 out1471.3133 XPM522 B

AaKKQEan…6be9ivsr APCLwsZN…Y9nxkbdb

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.

3.621 × 10⁹⁵(96-digit number)

36211526822012078367…78982217535465280959

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

3.621 × 10⁹⁵(96-digit number)

36211526822012078367…78982217535465280959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.621 × 10⁹⁵(96-digit number)

36211526822012078367…78982217535465280961

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

7.242 × 10⁹⁵(96-digit number)

72423053644024156735…57964435070930561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.242 × 10⁹⁵(96-digit number)

72423053644024156735…57964435070930561921

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

1.448 × 10⁹⁶(97-digit number)

14484610728804831347…15928870141861123839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.448 × 10⁹⁶(97-digit number)

14484610728804831347…15928870141861123841

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

2.896 × 10⁹⁶(97-digit number)

28969221457609662694…31857740283722247679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.896 × 10⁹⁶(97-digit number)

28969221457609662694…31857740283722247681

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

5.793 × 10⁹⁶(97-digit number)

57938442915219325388…63715480567444495359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.793 × 10⁹⁶(97-digit number)

57938442915219325388…63715480567444495361

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 #2,267,345

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