Block #2,642,066

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 2:26:40 PM · Difficulty 11.6409 · 4,188,896 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d38ecd2ce50318e16faaddc3f19eea7754ce35606c97b1c2c28c10e68b6ce6a6

View on Chainz ↗

Height

#2,642,066

Difficulty

11.640872

Transactions

Size

2.20 KB

Version

Bits

0ba41038

Nonce

417,766,895

Timestamp

5/1/2018, 2:26:40 PM

Confirmations

4,188,896

Mined by

⛏️ P2SHASpjEJsYGjKzJvYCMv1jLGWnZHbramkk4p

Merkle Root

ffb1ac8a98089c9fee4bb1f72f40247a32a03afdebf0036ed6284cc48ed87da2

Transactions (5)

Coinbase621070c1bf8036…ab1e2ed6c2da6f

1 in → 1 out7.4100 XPM110 B

ASpjEJsY…bramkk4p

20339793bd8e1a…df906e4374185c

3 in → 2 out555.2101 XPM523 B

ARF6b5Rk…1oFNwe5m AJ3vgUCe…Y8x9MiP5

970375bf452288…8b199233b1a347

1 in → 1 out3.9900 XPM193 B

ASEhqc6y…uiLW8tms

1d56e6d44fba29…9eaba1d86830c4

2 in → 2 out10.0900 XPM374 B

AbSu472H…8VvUY3w8 AaEjQAX5…tYpXQKZQ

930fecc5a22f37…53fa3bdb0cced0

6 in → 2 out4.0774 XPM966 B

AJ64A3i2…UjNpZxDY AJg5PF59…ypJgbvgo

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.

2.275 × 10⁹⁵(96-digit number)

22750680459445905235…84998074218005945599

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

2.275 × 10⁹⁵(96-digit number)

22750680459445905235…84998074218005945599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.275 × 10⁹⁵(96-digit number)

22750680459445905235…84998074218005945601

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

4.550 × 10⁹⁵(96-digit number)

45501360918891810471…69996148436011891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.550 × 10⁹⁵(96-digit number)

45501360918891810471…69996148436011891201

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

9.100 × 10⁹⁵(96-digit number)

91002721837783620943…39992296872023782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.100 × 10⁹⁵(96-digit number)

91002721837783620943…39992296872023782401

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

1.820 × 10⁹⁶(97-digit number)

18200544367556724188…79984593744047564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.820 × 10⁹⁶(97-digit number)

18200544367556724188…79984593744047564801

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

3.640 × 10⁹⁶(97-digit number)

36401088735113448377…59969187488095129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.640 × 10⁹⁶(97-digit number)

36401088735113448377…59969187488095129601

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

7.280 × 10⁹⁶(97-digit number)

72802177470226896754…19938374976190259199

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 #2,642,066

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