Block #2,782,995

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/7/2018, 7:43:20 AM · Difficulty 11.6606 · 4,058,997 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84d66bbc60309a978e449bbb7d79ce23cba6c4e7da2a7f05e2c3e422d6e524e9

View on Chainz ↗

Height

#2,782,995

Difficulty

11.660647

Transactions

Size

1.71 KB

Version

Bits

0ba92029

Nonce

573,543,548

Timestamp

8/7/2018, 7:43:20 AM

Confirmations

4,058,997

Mined by

⛏️ P2SHAJMwM6jpUtnoMsjVsW63Jvw62swzeS7tJs

Merkle Root

547d9360564b9351f8397b98fe00a9b6840f1d81ba4479734875ccfb28b31103

Transactions (2)

Coinbase2d2e37e115f57d…0fdfe2e7ecee8a

1 in → 1 out7.3600 XPM109 B

AJMwM6jp…wzeS7tJs

e3bfcdd6cc7937…32728e9c1a2d56

10 in → 2 out39.9800 XPM1.52 KB

AGLHtz2B…AssoJuj5 AGuEFTnh…SktbZx7R

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.

1.477 × 10⁹³(94-digit number)

14779798201975114800…37264109960644764599

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

1.477 × 10⁹³(94-digit number)

14779798201975114800…37264109960644764599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.477 × 10⁹³(94-digit number)

14779798201975114800…37264109960644764601

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

2.955 × 10⁹³(94-digit number)

29559596403950229601…74528219921289529199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.955 × 10⁹³(94-digit number)

29559596403950229601…74528219921289529201

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

5.911 × 10⁹³(94-digit number)

59119192807900459203…49056439842579058399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.911 × 10⁹³(94-digit number)

59119192807900459203…49056439842579058401

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

1.182 × 10⁹⁴(95-digit number)

11823838561580091840…98112879685158116799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.182 × 10⁹⁴(95-digit number)

11823838561580091840…98112879685158116801

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

2.364 × 10⁹⁴(95-digit number)

23647677123160183681…96225759370316233599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.364 × 10⁹⁴(95-digit number)

23647677123160183681…96225759370316233601

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

4.729 × 10⁹⁴(95-digit number)

47295354246320367362…92451518740632467199

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 #2,782,995

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