Block #2,851,885

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/23/2018, 11:01:35 AM · Difficulty 11.7246 · 3,985,034 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f95abdf8d2f32e9fa718c94576920ac3f6377001867ce356df071fe84237c3c2

View on Chainz ↗

Height

#2,851,885

Difficulty

11.724581

Transactions

Size

1.20 KB

Version

Bits

0bb97e2c

Nonce

938,684,395

Timestamp

9/23/2018, 11:01:35 AM

Confirmations

3,985,034

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

2a81015f5d6141b56d5547d851337479d58af2c6313cc42d55277759f65b39fd

Transactions (5)

Coinbaseebe8775f72d8ef…5897a444ac74dc

1 in → 1 out7.3000 XPM110 B

AUMQRepm…tAfKmdW1

ebfe67de4b1e4b…41234c14059845

2 in → 2 out14.4900 XPM306 B

APVKWthF…PMMxwRoz AXLGTbS7…7yg7vVru

36ed5d5ce505f2…c635eb1a8b6999

1 in → 2 out7.2400 XPM192 B

AamnkX56…Dk9c6QCr AZdr7aNw…MkNk9gCV

1b37d86c58786e…c680f00640608e

1 in → 2 out7.2400 XPM192 B

AdUxVBDa…ASpXLPok AKBxhYmY…4XGb9PCf

fd878d1f5e8669…024ce8d2519521

2 in → 2 out11.7400 XPM340 B

Aek7aQzY…4495YRvK ATUtL4BB…rbgPH24v

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.

2.260 × 10⁹⁵(96-digit number)

22603099281878233998…30528969460454489599

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

2.260 × 10⁹⁵(96-digit number)

22603099281878233998…30528969460454489599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.260 × 10⁹⁵(96-digit number)

22603099281878233998…30528969460454489601

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

4.520 × 10⁹⁵(96-digit number)

45206198563756467996…61057938920908979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.520 × 10⁹⁵(96-digit number)

45206198563756467996…61057938920908979201

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

9.041 × 10⁹⁵(96-digit number)

90412397127512935992…22115877841817958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.041 × 10⁹⁵(96-digit number)

90412397127512935992…22115877841817958401

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

1.808 × 10⁹⁶(97-digit number)

18082479425502587198…44231755683635916799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.808 × 10⁹⁶(97-digit number)

18082479425502587198…44231755683635916801

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

3.616 × 10⁹⁶(97-digit number)

36164958851005174396…88463511367271833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.616 × 10⁹⁶(97-digit number)

36164958851005174396…88463511367271833601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.232 × 10⁹⁶(97-digit number)

72329917702010348793…76927022734543667199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,851,885

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