Block #2,649,831

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 1:24:37 PM · Difficulty 11.7620 · 4,183,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e880969f2d446ffb9d5442592bcf402e697efe58590cd18fc8588b7db25971a

View on Chainz ↗

Height

#2,649,831

Difficulty

11.761964

Transactions

Size

619 B

Version

Bits

0bc31016

Nonce

844,835,738

Timestamp

5/5/2018, 1:24:37 PM

Confirmations

4,183,966

Mined by

⛏️ P2SHAawWbnDvV3YzmJLUXQjR8V46wHyQWbGYJu

Merkle Root

8bb18ec3dd643a13708ed459f43f9bcc0e139babd54a06242ded714968ecd212

Transactions (3)

Coinbase1b820b66387b5e…d11232dbcfbade

1 in → 1 out7.2400 XPM110 B

AawWbnDv…yQWbGYJu

ad67114abbf690…149efa6afda0d4

1 in → 2 out7.2200 XPM192 B

AKkA4NAB…Qrms46Am AQJNygdQ…PMXUCooh

f57c4d160183c2…e944b252a007bb

1 in → 2 out5.1880 XPM227 B

AdKhEL4Q…RQS9ZydR AHNyWNBc…PPJpaUAC

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.

2.245 × 10⁹⁵(96-digit number)

22455820534903964468…32000459293437373759

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

2.245 × 10⁹⁵(96-digit number)

22455820534903964468…32000459293437373759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.245 × 10⁹⁵(96-digit number)

22455820534903964468…32000459293437373761

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

4.491 × 10⁹⁵(96-digit number)

44911641069807928936…64000918586874747519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.491 × 10⁹⁵(96-digit number)

44911641069807928936…64000918586874747521

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

8.982 × 10⁹⁵(96-digit number)

89823282139615857872…28001837173749495039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.982 × 10⁹⁵(96-digit number)

89823282139615857872…28001837173749495041

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

1.796 × 10⁹⁶(97-digit number)

17964656427923171574…56003674347498990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.796 × 10⁹⁶(97-digit number)

17964656427923171574…56003674347498990081

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

3.592 × 10⁹⁶(97-digit number)

35929312855846343149…12007348694997980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.592 × 10⁹⁶(97-digit number)

35929312855846343149…12007348694997980161

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

7.185 × 10⁹⁶(97-digit number)

71858625711692686298…24014697389995960319

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 #2,649,831

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