Block #2,784,841

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/8/2018, 12:22:40 PM · Difficulty 11.6691 · 4,041,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69e99da7728de52912bf4e5d5ef2c1c83fa9215b9958712d261ca199572c1e9d

View on Chainz ↗

Height

#2,784,841

Difficulty

11.669106

Transactions

Size

1.03 KB

Version

Bits

0bab4a8f

Nonce

285,858,243

Timestamp

8/8/2018, 12:22:40 PM

Confirmations

4,041,391

Mined by

⛏️ P2SHAYpghNnAFVfL6wc1wy4vrQDjj7qjoSCft4

Merkle Root

0f6e2f48aeae2c88556b98a46d5ddefb4f096ea05fb4facde56b0d1e70ab452b

Transactions (2)

Coinbaseb8aa08faf9353a…72a9cc3708a6ca

1 in → 1 out7.3400 XPM110 B

AYpghNnA…qjoSCft4

909787a6040b29…8f530dd90ad4f8

5 in → 3 out7.3159 XPM851 B

AKVLpTzR…HbpmwEXs ASk9H3sY…qUG8r1d4 APi8C85f…Lg5MDiei

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.

3.231 × 10⁹⁴(95-digit number)

32318184041785156536…69826448130746461439

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

3.231 × 10⁹⁴(95-digit number)

32318184041785156536…69826448130746461439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.231 × 10⁹⁴(95-digit number)

32318184041785156536…69826448130746461441

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

6.463 × 10⁹⁴(95-digit number)

64636368083570313073…39652896261492922879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.463 × 10⁹⁴(95-digit number)

64636368083570313073…39652896261492922881

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

1.292 × 10⁹⁵(96-digit number)

12927273616714062614…79305792522985845759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.292 × 10⁹⁵(96-digit number)

12927273616714062614…79305792522985845761

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

2.585 × 10⁹⁵(96-digit number)

25854547233428125229…58611585045971691519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.585 × 10⁹⁵(96-digit number)

25854547233428125229…58611585045971691521

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

5.170 × 10⁹⁵(96-digit number)

51709094466856250458…17223170091943383039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.170 × 10⁹⁵(96-digit number)

51709094466856250458…17223170091943383041

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

1.034 × 10⁹⁶(97-digit number)

10341818893371250091…34446340183886766079

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.034 × 10⁹⁶(97-digit number)

10341818893371250091…34446340183886766081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,784,841

Cookie Preferences