Block #2,654,833

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/9/2018, 4:16:16 PM · Difficulty 11.7139 · 4,183,684 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58cc93be0d6b980804197f3c3cac21a119cc756dd306c7d5252c2f1052906dc6

View on Chainz ↗

Height

#2,654,833

Difficulty

11.713899

Transactions

Size

1.19 KB

Version

Bits

0bb6c210

Nonce

93,879,162

Timestamp

5/9/2018, 4:16:16 PM

Confirmations

4,183,684

Mined by

⛏️ P2SHASqG9LNtmohX2mmJ9peaKU9mVosH6yDP6n

Merkle Root

8cc7c9412507f5915e8242120888f8bfbf4bcb43c7db94bd16b3b570883abe5e

Transactions (5)

Coinbase9d4a879e2d9e88…d8091ac316dcdf

1 in → 1 out7.3200 XPM110 B

ASqG9LNt…sH6yDP6n

fbbd19d03593d3…cb541061fb4a7e

1 in → 2 out7.2100 XPM192 B

AHvDkCvW…ES8pnYEn AUwDpfD1…xk9rAByg

8e873e2387ee7a…1e88454d04a21d

1 in → 2 out1.2933 XPM227 B

AVp6yxXk…M3EF5f4G AWp4iAg7…FUBLEm8x

505b0e0107d725…77dcf31d793aa3

1 in → 2 out1.2156 XPM226 B

ARod15qD…RM2kuBZD ARb4rLcS…HNnqv3of

3e2219abc4a37d…13c788d3d7a5ef

2 in → 2 out1.0658 XPM372 B

AMXJYDqH…1B6ShWF3 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.

1.532 × 10⁹⁷(98-digit number)

15323171822101110066…82913047393390264319

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

1.532 × 10⁹⁷(98-digit number)

15323171822101110066…82913047393390264319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.532 × 10⁹⁷(98-digit number)

15323171822101110066…82913047393390264321

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

3.064 × 10⁹⁷(98-digit number)

30646343644202220132…65826094786780528639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.064 × 10⁹⁷(98-digit number)

30646343644202220132…65826094786780528641

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

6.129 × 10⁹⁷(98-digit number)

61292687288404440265…31652189573561057279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.129 × 10⁹⁷(98-digit number)

61292687288404440265…31652189573561057281

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

1.225 × 10⁹⁸(99-digit number)

12258537457680888053…63304379147122114559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.225 × 10⁹⁸(99-digit number)

12258537457680888053…63304379147122114561

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

2.451 × 10⁹⁸(99-digit number)

24517074915361776106…26608758294244229119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.451 × 10⁹⁸(99-digit number)

24517074915361776106…26608758294244229121

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

4.903 × 10⁹⁸(99-digit number)

49034149830723552212…53217516588488458239

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 #2,654,833

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