Block #2,762,909

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/24/2018, 10:05:41 AM · Difficulty 11.6553 · 4,074,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

338f8fb4c874c5666013422b08c7cfd009b43d600808181e95e48b9c13398655

View on Chainz ↗

Height

#2,762,909

Difficulty

11.655342

Transactions

Size

722 B

Version

Bits

0ba7c485

Nonce

390,603,905

Timestamp

7/24/2018, 10:05:41 AM

Confirmations

4,074,366

Mined by

⛏️ P2SHAUaZXv54PtWk8kmoUEqLhnrpPRsEtGVeuz

Merkle Root

edbe64e934a6f288609e59670d4082f7dd71950d59544d4c725f888e41b66774

Transactions (2)

Coinbase20fbc592b6c492…a1b776987b2e51

1 in → 1 out7.3700 XPM110 B

AUaZXv54…sEtGVeuz

bf3aaf03794f98…6ca4294c2542fc

3 in → 2 out279.6399 XPM521 B

AbiZw7N1…HPacQJfk ARzCcvJp…oLdpwMFu

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.

8.907 × 10⁹⁵(96-digit number)

89078860187763470687…07038485995160314879

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

8.907 × 10⁹⁵(96-digit number)

89078860187763470687…07038485995160314879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.907 × 10⁹⁵(96-digit number)

89078860187763470687…07038485995160314881

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

1.781 × 10⁹⁶(97-digit number)

17815772037552694137…14076971990320629759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.781 × 10⁹⁶(97-digit number)

17815772037552694137…14076971990320629761

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

3.563 × 10⁹⁶(97-digit number)

35631544075105388275…28153943980641259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.563 × 10⁹⁶(97-digit number)

35631544075105388275…28153943980641259521

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

7.126 × 10⁹⁶(97-digit number)

71263088150210776550…56307887961282519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.126 × 10⁹⁶(97-digit number)

71263088150210776550…56307887961282519041

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

1.425 × 10⁹⁷(98-digit number)

14252617630042155310…12615775922565038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.425 × 10⁹⁷(98-digit number)

14252617630042155310…12615775922565038081

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

2.850 × 10⁹⁷(98-digit number)

28505235260084310620…25231551845130076159

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 #2,762,909

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