Block #3,227,404

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/16/2019, 6:03:34 AM · Difficulty 11.0074 · 3,605,809 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d4ea712b258f3ed6afb37f874094f21f754c1a4e75f5d7df3c83d504483bab2

View on Chainz ↗

Height

#3,227,404

Difficulty

11.007367

Transactions

Size

1016 B

Version

Bits

0b01e2c8

Nonce

497,789,028

Timestamp

6/16/2019, 6:03:34 AM

Confirmations

3,605,809

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

4bf8cf33658380250f077ca61e98d5caff602225e166e0a914897a86e769037a

Transactions (2)

Coinbaseec250d21963fcc…936c49be89dacd

1 in → 1 out8.2600 XPM110 B

AbXwmGxD…4XXYP765

e6829b70fd13f6…4e16c97ab9545b

5 in → 2 out963.3064 XPM817 B

AQpirNZH…YMX3K11g AKPhMRzB…eUYgAhqb

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.

3.338 × 10⁹³(94-digit number)

33381634184657858122…98402948744651664259

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

3.338 × 10⁹³(94-digit number)

33381634184657858122…98402948744651664259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.338 × 10⁹³(94-digit number)

33381634184657858122…98402948744651664261

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

6.676 × 10⁹³(94-digit number)

66763268369315716244…96805897489303328519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.676 × 10⁹³(94-digit number)

66763268369315716244…96805897489303328521

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

1.335 × 10⁹⁴(95-digit number)

13352653673863143248…93611794978606657039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.335 × 10⁹⁴(95-digit number)

13352653673863143248…93611794978606657041

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

2.670 × 10⁹⁴(95-digit number)

26705307347726286497…87223589957213314079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.670 × 10⁹⁴(95-digit number)

26705307347726286497…87223589957213314081

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

5.341 × 10⁹⁴(95-digit number)

53410614695452572995…74447179914426628159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.341 × 10⁹⁴(95-digit number)

53410614695452572995…74447179914426628161

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

1.068 × 10⁹⁵(96-digit number)

10682122939090514599…48894359828853256319

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 #3,227,404

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