Block #3,242,279

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/26/2019, 9:15:23 PM · Difficulty 11.0018 · 3,600,450 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

135334e25b07bf5a0c8031692d8e5e3481ce4c6102ac9e4a79416bd15a9f5d1e

View on Chainz ↗

Height

#3,242,279

Difficulty

11.001830

Transactions

Size

990 B

Version

Bits

0b0077e6

Nonce

828,611,063

Timestamp

6/26/2019, 9:15:23 PM

Confirmations

3,600,450

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

2a2373a9534f3f3b2468520fce1e2e479a409c1e93bdbeede3c0eacb1e9d4a91

Transactions (4)

Coinbasef06e8be36b38e6…e67b2016494b5f

1 in → 1 out8.2800 XPM110 B

ASiq2qtK…VMhmk7yL

aadf0af328c023…2bd14b9db5d47a

2 in → 2 out15.4502 XPM338 B

AdGFnV3a…o6n2zX3x ASiq2qtK…VMhmk7yL

fd4381c793d428…a6ae14114b565e

1 in → 2 out6.4398 XPM227 B

AKpMPYXA…ia58Sytm ASiq2qtK…VMhmk7yL

51444c220becce…fff8f642c11cc4

1 in → 2 out4.6189 XPM225 B

AJtQNmM4…XBRjaQ6m ASiq2qtK…VMhmk7yL

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.

3.113 × 10⁹⁵(96-digit number)

31138221926389121207…91521623613745151999

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

3.113 × 10⁹⁵(96-digit number)

31138221926389121207…91521623613745151999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.113 × 10⁹⁵(96-digit number)

31138221926389121207…91521623613745152001

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

6.227 × 10⁹⁵(96-digit number)

62276443852778242414…83043247227490303999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.227 × 10⁹⁵(96-digit number)

62276443852778242414…83043247227490304001

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

1.245 × 10⁹⁶(97-digit number)

12455288770555648482…66086494454980607999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.245 × 10⁹⁶(97-digit number)

12455288770555648482…66086494454980608001

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

2.491 × 10⁹⁶(97-digit number)

24910577541111296965…32172988909961215999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.491 × 10⁹⁶(97-digit number)

24910577541111296965…32172988909961216001

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

4.982 × 10⁹⁶(97-digit number)

49821155082222593931…64345977819922431999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.982 × 10⁹⁶(97-digit number)

49821155082222593931…64345977819922432001

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

9.964 × 10⁹⁶(97-digit number)

99642310164445187862…28691955639844863999

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 #3,242,279

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