Block #2,685,920

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/31/2018, 1:57:18 PM · Difficulty 11.6880 · 4,151,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c25a580dc0afbd2e4e465d0b3abebf2ef2279fa2424f2c9bddeec2c80c09d143

View on Chainz ↗

Height

#2,685,920

Difficulty

11.687991

Transactions

Size

1.28 KB

Version

Bits

0bb02030

Nonce

272,383,302

Timestamp

5/31/2018, 1:57:18 PM

Confirmations

4,151,010

Mined by

⛏️ P2SHAJTPxHkd2RRJBW6QXwapwEkdbu7eTD4tFN

Merkle Root

6c529b6e34ec9dd74217611d6a3885eb3dfd285d73ed99f7a05a3e9d7389eeca

Transactions (2)

Coinbaseafdcfd8adf2672…6d736ce10b040a

1 in → 1 out7.3300 XPM110 B

AJTPxHkd…7eTD4tFN

e6a436884ccab6…4af04aad06f44b

7 in → 2 out12200.0000 XPM1.08 KB

APSALzPq…oMrnQiqA ARQBQiFS…uxviAzfZ

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.

4.178 × 10⁹⁵(96-digit number)

41783633305739907504…83840660162714664959

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

4.178 × 10⁹⁵(96-digit number)

41783633305739907504…83840660162714664959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.178 × 10⁹⁵(96-digit number)

41783633305739907504…83840660162714664961

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

8.356 × 10⁹⁵(96-digit number)

83567266611479815008…67681320325429329919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.356 × 10⁹⁵(96-digit number)

83567266611479815008…67681320325429329921

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

1.671 × 10⁹⁶(97-digit number)

16713453322295963001…35362640650858659839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.671 × 10⁹⁶(97-digit number)

16713453322295963001…35362640650858659841

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

3.342 × 10⁹⁶(97-digit number)

33426906644591926003…70725281301717319679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.342 × 10⁹⁶(97-digit number)

33426906644591926003…70725281301717319681

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

6.685 × 10⁹⁶(97-digit number)

66853813289183852007…41450562603434639359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.685 × 10⁹⁶(97-digit number)

66853813289183852007…41450562603434639361

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

1.337 × 10⁹⁷(98-digit number)

13370762657836770401…82901125206869278719

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 #2,685,920

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