Block #2,795,865

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/16/2018, 1:00:33 AM · Difficulty 11.6816 · 4,043,442 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b27214bb8feb42b65b143f91cd6a113894312818aae9b91b8592b3110f7a6f51

View on Chainz ↗

Height

#2,795,865

Difficulty

11.681589

Transactions

Size

2.18 KB

Version

Bits

0bae7ca6

Nonce

1,632,316,884

Timestamp

8/16/2018, 1:00:33 AM

Confirmations

4,043,442

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

1a4d57407e7e8e107436a123b6a7f1a06f05f8d57a387356abda04f533d93997

Transactions (5)

Coinbase3de5b8bfb91f42…cd279c324961f0

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

704452345ced15…46a24ee2b03ec1

1 in → 2 out7.3100 XPM191 B

AM5S7zCR…DQCoNK6w AMv64uDT…aEqYvY3e

44f918c1c21b32…9abfd292b11b20

1 in → 2 out7.3100 XPM192 B

ALEKNWbH…2i4mTz3h ALcLLBQ6…WYfR2N9m

1d14e3b8809607…ab00a860e9e798

10 in → 2 out32.0856 XPM1.39 KB

AWp4iAg7…FUBLEm8x AQs8Gpa5…wXXZxHrz

b2a7ea2afd484e…c6a7ab29ab0393

1 in → 2 out6.2920 XPM226 B

AKanrQFV…vieTTsaC AdhZKz3C…PCNoHLWE

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.

1.209 × 10⁹²(93-digit number)

12094679954219803208…81286320906752300239

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

1.209 × 10⁹²(93-digit number)

12094679954219803208…81286320906752300239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.209 × 10⁹²(93-digit number)

12094679954219803208…81286320906752300241

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

2.418 × 10⁹²(93-digit number)

24189359908439606417…62572641813504600479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.418 × 10⁹²(93-digit number)

24189359908439606417…62572641813504600481

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

4.837 × 10⁹²(93-digit number)

48378719816879212834…25145283627009200959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.837 × 10⁹²(93-digit number)

48378719816879212834…25145283627009200961

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

9.675 × 10⁹²(93-digit number)

96757439633758425668…50290567254018401919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.675 × 10⁹²(93-digit number)

96757439633758425668…50290567254018401921

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

1.935 × 10⁹³(94-digit number)

19351487926751685133…00581134508036803839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.935 × 10⁹³(94-digit number)

19351487926751685133…00581134508036803841

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

3.870 × 10⁹³(94-digit number)

38702975853503370267…01162269016073607679

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 #2,795,865

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