Block #2,650,204

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 8:47:26 PM · Difficulty 11.7586 · 4,189,148 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ad6e490de44c6a716bf36f0302519ed5e8f09dafb42877114879a25fef8ea8d

View on Chainz ↗

Height

#2,650,204

Difficulty

11.758578

Transactions

Size

1016 B

Version

Bits

0bc23227

Nonce

207,834,154

Timestamp

5/5/2018, 8:47:26 PM

Confirmations

4,189,148

Mined by

⛏️ P2SHARNgiHmvj1heJ3ty36gH13GLikKUF2nCm7

Merkle Root

f1e89b0f3c22d3a3d0dd4f9ef7d5d2cd4ffd32315efc2ff8200bfbc2ce0c0338

Transactions (2)

Coinbase8c5d9737bf0512…389f657e0a33ee

1 in → 1 out7.2400 XPM110 B

ARNgiHmv…KUF2nCm7

94248cf24bfd36…b5ad762d6b6f85

5 in → 2 out1050.0101 XPM816 B

AGXfmTUj…TwqYUaHa AQNguhqN…ELQ9NTs8

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.

1.389 × 10⁹⁴(95-digit number)

13892263270030303655…61271987123372603039

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

1.389 × 10⁹⁴(95-digit number)

13892263270030303655…61271987123372603039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.389 × 10⁹⁴(95-digit number)

13892263270030303655…61271987123372603041

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

2.778 × 10⁹⁴(95-digit number)

27784526540060607311…22543974246745206079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.778 × 10⁹⁴(95-digit number)

27784526540060607311…22543974246745206081

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

5.556 × 10⁹⁴(95-digit number)

55569053080121214622…45087948493490412159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.556 × 10⁹⁴(95-digit number)

55569053080121214622…45087948493490412161

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

1.111 × 10⁹⁵(96-digit number)

11113810616024242924…90175896986980824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.111 × 10⁹⁵(96-digit number)

11113810616024242924…90175896986980824321

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

2.222 × 10⁹⁵(96-digit number)

22227621232048485848…80351793973961648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.222 × 10⁹⁵(96-digit number)

22227621232048485848…80351793973961648641

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

4.445 × 10⁹⁵(96-digit number)

44455242464096971697…60703587947923297279

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 #2,650,204

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