Block #2,487,571

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/24/2018, 6:10:12 AM · Difficulty 10.9693 · 4,355,902 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e667e680ba8d28b9ef96e8b5812beb1a93109a2286008a1bce661844fddb22a

View on Chainz ↗

Height

#2,487,571

Difficulty

10.969278

Transactions

Size

35.38 KB

Version

Bits

0af822a1

Nonce

1,112,964,666

Timestamp

1/24/2018, 6:10:12 AM

Confirmations

4,355,902

Mined by

⛏️ P2SHAJgYZcRqLYdknHS8xX5wtkMKSLSNPeGAr8

Merkle Root

58d51ac2477997a898d45a3293a38df8ee6b5611ae867e06c9ec570799d32e9c

Transactions (2)

Coinbasecf001bbebda69d…c51db89812b742

1 in → 1 out8.6700 XPM110 B

AJgYZcRq…SNPeGAr8

1410e021915e29…b560f2ddc13cdc

243 in → 1 out1093.4622 XPM35.18 KB

ATNFg4tq…AMdaKJFH

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.

8.693 × 10⁹⁵(96-digit number)

86939712678251943886…37987182037090147199

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

8.693 × 10⁹⁵(96-digit number)

86939712678251943886…37987182037090147199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.693 × 10⁹⁵(96-digit number)

86939712678251943886…37987182037090147201

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

1.738 × 10⁹⁶(97-digit number)

17387942535650388777…75974364074180294399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.738 × 10⁹⁶(97-digit number)

17387942535650388777…75974364074180294401

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

3.477 × 10⁹⁶(97-digit number)

34775885071300777554…51948728148360588799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.477 × 10⁹⁶(97-digit number)

34775885071300777554…51948728148360588801

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

6.955 × 10⁹⁶(97-digit number)

69551770142601555109…03897456296721177599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.955 × 10⁹⁶(97-digit number)

69551770142601555109…03897456296721177601

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

1.391 × 10⁹⁷(98-digit number)

13910354028520311021…07794912593442355199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.391 × 10⁹⁷(98-digit number)

13910354028520311021…07794912593442355201

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

2.782 × 10⁹⁷(98-digit number)

27820708057040622043…15589825186884710399

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 #2,487,571

Cookie Preferences