Block #2,689,730

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/3/2018, 7:25:41 AM · Difficulty 11.6808 · 4,155,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

844a11002001000d87742819e00903b5f6cc8fcd0b35ecc157bfddd34f391052

View on Chainz ↗

Height

#2,689,730

Difficulty

11.680769

Transactions

Size

1.93 KB

Version

Bits

0bae46de

Nonce

102,536,948

Timestamp

6/3/2018, 7:25:41 AM

Confirmations

4,155,173

Mined by

⛏️ P2SHASnPtmWyhpep5tQ61V3mWmGBNqnnzvQwh9

Merkle Root

cd122040745820aa8281d620f5c410bcf6e4e0e4502184bd0be3fc0730fde101

Transactions (5)

Coinbase0e50d266c5c844…6d4863fe86bb43

1 in → 1 out7.3600 XPM110 B

ASnPtmWy…nnzvQwh9

8b737285d6a856…a178a7e5174002

1 in → 2 out7.3000 XPM192 B

AQwyw2q9…jei7cTFz AUHBKKGB…mR5KpgvJ

f796ca526362e7…ec9a75261b4e87

7 in → 2 out33.1211 XPM978 B

AWp4iAg7…FUBLEm8x AJsRVKgn…KVPMG7Jd

e961a1c1648c89…20c53badd9e3dd

2 in → 2 out1.1188 XPM375 B

AHtKGoRa…s5Shmq9n AVftt1bk…L6AuHtJz

f017b07505b2dc…833b672244d32d

1 in → 2 out3.2853 XPM227 B

AZio5CrN…65k6BJk3 ATmBmi6s…NU3bWEyy

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.

1.372 × 10⁹⁶(97-digit number)

13728483894433000431…42160776147414181759

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

1.372 × 10⁹⁶(97-digit number)

13728483894433000431…42160776147414181759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.372 × 10⁹⁶(97-digit number)

13728483894433000431…42160776147414181761

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

2.745 × 10⁹⁶(97-digit number)

27456967788866000863…84321552294828363519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.745 × 10⁹⁶(97-digit number)

27456967788866000863…84321552294828363521

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

5.491 × 10⁹⁶(97-digit number)

54913935577732001726…68643104589656727039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.491 × 10⁹⁶(97-digit number)

54913935577732001726…68643104589656727041

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

1.098 × 10⁹⁷(98-digit number)

10982787115546400345…37286209179313454079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.098 × 10⁹⁷(98-digit number)

10982787115546400345…37286209179313454081

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

2.196 × 10⁹⁷(98-digit number)

21965574231092800690…74572418358626908159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.196 × 10⁹⁷(98-digit number)

21965574231092800690…74572418358626908161

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

4.393 × 10⁹⁷(98-digit number)

43931148462185601381…49144836717253816319

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 #2,689,730

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