Block #2,680,326

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/27/2018, 3:38:34 PM · Difficulty 11.6918 · 4,156,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06ce4d846302dc404ce1876331dc1512d41009555d60af95d250d56b95225f9b

View on Chainz ↗

Height

#2,680,326

Difficulty

11.691777

Transactions

Size

2.22 KB

Version

Bits

0bb11844

Nonce

83,856,659

Timestamp

5/27/2018, 3:38:34 PM

Confirmations

4,156,191

Mined by

⛏️ P2SHAGi6Kc2hmd3pT1cEPtmA4njzbt12ofmZYu

Merkle Root

b0ff6c06758f8a0daf016a4b870bf82f509731f29eecd1c64ed72127b951b455

Transactions (5)

Coinbase5ec70481116bd5…351d28ac8bf893

1 in → 1 out7.3500 XPM110 B

AGi6Kc2h…12ofmZYu

73cb235c7bbc22…8bf54f81628f2b

1 in → 2 out7.2900 XPM191 B

AaxEyUSy…DV4Wx2fD AN7b55gz…YroqkbjU

e75ec9c2133123…65992a10660c8b

1 in → 2 out7.2900 XPM192 B

AejuQx54…cTTJyuwS AV3JM4zu…4Yqk98pg

7d40f0bdf5b4fa…a80c3882ecebdc

10 in → 2 out34.2625 XPM1.43 KB

AWp4iAg7…FUBLEm8x Aa5fQMfE…XTE7u97o

33ae8fecf7078f…5f58353caeea25

1 in → 2 out2.2524 XPM227 B

AMgyKXdm…GwmikJTL ASQdb5nP…7oSVGsmb

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.

1.314 × 10⁹⁴(95-digit number)

13143268853933399345…23359442317835436799

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

1.314 × 10⁹⁴(95-digit number)

13143268853933399345…23359442317835436799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.314 × 10⁹⁴(95-digit number)

13143268853933399345…23359442317835436801

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

2.628 × 10⁹⁴(95-digit number)

26286537707866798690…46718884635670873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.628 × 10⁹⁴(95-digit number)

26286537707866798690…46718884635670873601

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

5.257 × 10⁹⁴(95-digit number)

52573075415733597381…93437769271341747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.257 × 10⁹⁴(95-digit number)

52573075415733597381…93437769271341747201

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

1.051 × 10⁹⁵(96-digit number)

10514615083146719476…86875538542683494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.051 × 10⁹⁵(96-digit number)

10514615083146719476…86875538542683494401

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

2.102 × 10⁹⁵(96-digit number)

21029230166293438952…73751077085366988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.102 × 10⁹⁵(96-digit number)

21029230166293438952…73751077085366988801

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

4.205 × 10⁹⁵(96-digit number)

42058460332586877905…47502154170733977599

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 #2,680,326

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