Block #2,656,805

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/11/2018, 9:33:29 AM · Difficulty 11.6839 · 4,180,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d4f11495cbd5d4b542c95e6420c62d92a514822d8c9621cef36eb2049198391

View on Chainz ↗

Height

#2,656,805

Difficulty

11.683880

Transactions

Size

1.74 KB

Version

Bits

0baf12c3

Nonce

494,407,997

Timestamp

5/11/2018, 9:33:29 AM

Confirmations

4,180,058

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

07536b79b7e54315a1702592c5fcb8b4f5f1c3cc70b1ed3609eae511a19efdcf

Transactions (5)

Coinbase545fc52553b81b…2f29a334612196

1 in → 1 out7.3600 XPM110 B

Adqah8zh…1WwoHJ9t

96c4f047f45c54…eded655ce36de2

4 in → 2 out9957.8600 XPM669 B

ATGPBLmo…CFXDY7bV AK3WjKqK…Nd1tQXSj

aeb396a8347856…aee526d531f49e

2 in → 2 out14.4900 XPM305 B

APVKWthF…PMMxwRoz AZSFMDHa…mhaVoEcE

d77e40fdc60b7f…fd26283b991b0f

2 in → 2 out14.4900 XPM306 B

AYQUEruW…ZqhFg4u7 AWUp78nX…vr1EiuXy

d8544a841e2fba…7c32790b296abe

2 in → 2 out14.4900 XPM306 B

AW3QZZmg…j2rGjUkp AYVmuFAw…TbGb2vNg

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.

1.716 × 10⁹³(94-digit number)

17169502854569869981…23022502134769816759

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

1.716 × 10⁹³(94-digit number)

17169502854569869981…23022502134769816759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.716 × 10⁹³(94-digit number)

17169502854569869981…23022502134769816761

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

3.433 × 10⁹³(94-digit number)

34339005709139739963…46045004269539633519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.433 × 10⁹³(94-digit number)

34339005709139739963…46045004269539633521

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

6.867 × 10⁹³(94-digit number)

68678011418279479927…92090008539079267039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.867 × 10⁹³(94-digit number)

68678011418279479927…92090008539079267041

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

1.373 × 10⁹⁴(95-digit number)

13735602283655895985…84180017078158534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.373 × 10⁹⁴(95-digit number)

13735602283655895985…84180017078158534081

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

2.747 × 10⁹⁴(95-digit number)

27471204567311791971…68360034156317068159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.747 × 10⁹⁴(95-digit number)

27471204567311791971…68360034156317068161

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

5.494 × 10⁹⁴(95-digit number)

54942409134623583942…36720068312634136319

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 #2,656,805

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