Block #2,641,933

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 1:06:13 PM · Difficulty 11.6371 · 4,197,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9524a27042ec8135b50418ae04da682075b83fbc4e9c185e7fb84dad1ca544e

View on Chainz ↗

Height

#2,641,933

Difficulty

11.637078

Transactions

Size

876 B

Version

Bits

0ba31789

Nonce

1,883,127,801

Timestamp

5/1/2018, 1:06:13 PM

Confirmations

4,197,018

Mined by

⛏️ P2SHASE4BP8ot5y2nsicHaxsLpH786k5Ld5m1x

Merkle Root

ea8d0a283d980ac296cce93605d8d8f142b48b200be5b71b9c10f0d9bd8bd94c

Transactions (4)

Coinbase1bcaa12b05df36…d3cde8586d7ec9

1 in → 1 out7.4000 XPM110 B

ASE4BP8o…k5Ld5m1x

98de41fb221858…48b2fd593fbdf1

1 in → 2 out1206.3025 XPM225 B

AJ3vgUCe…Y8x9MiP5 AKY88AxH…BFAzgNiZ

1a49ada89bf810…2b9d57a4b609be

1 in → 2 out2.5167 XPM225 B

ARVB3VhP…oiWMhgNG AMFxoiZV…2UX5WRMn

8b1fc3a20d3f3f…71eebfd9046862

1 in → 2 out1.2354 XPM226 B

AcjL91Ge…hpQ8Yn7N AGaku26r…JYV3fSSU

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.

5.790 × 10⁹⁵(96-digit number)

57906869334016444166…42817004133166988799

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

5.790 × 10⁹⁵(96-digit number)

57906869334016444166…42817004133166988799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.790 × 10⁹⁵(96-digit number)

57906869334016444166…42817004133166988801

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

1.158 × 10⁹⁶(97-digit number)

11581373866803288833…85634008266333977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.158 × 10⁹⁶(97-digit number)

11581373866803288833…85634008266333977601

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

2.316 × 10⁹⁶(97-digit number)

23162747733606577666…71268016532667955199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.316 × 10⁹⁶(97-digit number)

23162747733606577666…71268016532667955201

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

4.632 × 10⁹⁶(97-digit number)

46325495467213155333…42536033065335910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.632 × 10⁹⁶(97-digit number)

46325495467213155333…42536033065335910401

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

9.265 × 10⁹⁶(97-digit number)

92650990934426310666…85072066130671820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.265 × 10⁹⁶(97-digit number)

92650990934426310666…85072066130671820801

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

1.853 × 10⁹⁷(98-digit number)

18530198186885262133…70144132261343641599

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 #2,641,933

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