Block #2,823,033

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/3/2018, 4:04:05 PM · Difficulty 11.7035 · 4,010,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

73c90e762e6f35cdd4afff3283f926ff7ffb53e674a4528247d649b20a958be8

View on Chainz ↗

Height

#2,823,033

Difficulty

11.703464

Transactions

Size

1019 B

Version

Bits

0bb4163d

Nonce

342,792,643

Timestamp

9/3/2018, 4:04:05 PM

Confirmations

4,010,272

Mined by

⛏️ P2SHAGepYXmbRngB6VD5eLz5vhYn9JC79oTTaQ

Merkle Root

cd70a2366a60b3ee7df380d6e4b50de1455e27709244fc7de0b7028a8d90475e

Transactions (2)

Coinbasee921f5fdec83ae…cbd46540fd44a4

1 in → 1 out7.3000 XPM110 B

AGepYXmb…C79oTTaQ

c66c475b092a05…edb04b796f3fe3

5 in → 2 out528.0130 XPM817 B

AbCdGpym…k3wfrCNw AJCe6S8t…geJbi4Ae

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.

4.752 × 10⁹⁸(99-digit number)

47522909627749110973…69222485860601692159

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

4.752 × 10⁹⁸(99-digit number)

47522909627749110973…69222485860601692159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.752 × 10⁹⁸(99-digit number)

47522909627749110973…69222485860601692161

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

9.504 × 10⁹⁸(99-digit number)

95045819255498221947…38444971721203384319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.504 × 10⁹⁸(99-digit number)

95045819255498221947…38444971721203384321

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

1.900 × 10⁹⁹(100-digit number)

19009163851099644389…76889943442406768639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.900 × 10⁹⁹(100-digit number)

19009163851099644389…76889943442406768641

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

3.801 × 10⁹⁹(100-digit number)

38018327702199288779…53779886884813537279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.801 × 10⁹⁹(100-digit number)

38018327702199288779…53779886884813537281

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

7.603 × 10⁹⁹(100-digit number)

76036655404398577558…07559773769627074559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.603 × 10⁹⁹(100-digit number)

76036655404398577558…07559773769627074561

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

1.520 × 10¹⁰⁰(101-digit number)

15207331080879715511…15119547539254149119

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 #2,823,033

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