Block #3,033,101

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/31/2019, 4:12:39 PM · Difficulty 11.0527 · 3,811,387 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41732585f75a766ede5471ac89c2f9a34b55952c028960ef32ea5f3598dab23f

View on Chainz ↗

Height

#3,033,101

Difficulty

11.052683

Transactions

Size

1.64 KB

Version

Bits

0b0d7ca4

Nonce

418,776,993

Timestamp

1/31/2019, 4:12:39 PM

Confirmations

3,811,387

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

67a146ba63f0f728393ff6c27b5b08f570f4e8d4a184680e0bec237cc43c4dc1

Transactions (3)

Coinbasef7aa2fe5e42abe…2f9abff6efcb55

1 in → 1 out8.2000 XPM109 B

AUMQRepm…tAfKmdW1

3dfe0fb7206adf…d5b4da143fbb1f

9 in → 2 out71.5956 XPM1.11 KB

AXeaisCp…JHSFtiZf AbXwmGxD…4XXYP765

aaac1cf81b0784…651f3e335b05b1

2 in → 2 out13.5979 XPM341 B

AbXwmGxD…4XXYP765 AdGFnV3a…o6n2zX3x

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.

1.031 × 10⁹⁴(95-digit number)

10311041529738511221…78597915052651281919

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

1.031 × 10⁹⁴(95-digit number)

10311041529738511221…78597915052651281919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.031 × 10⁹⁴(95-digit number)

10311041529738511221…78597915052651281921

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

2.062 × 10⁹⁴(95-digit number)

20622083059477022443…57195830105302563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.062 × 10⁹⁴(95-digit number)

20622083059477022443…57195830105302563841

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

4.124 × 10⁹⁴(95-digit number)

41244166118954044886…14391660210605127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.124 × 10⁹⁴(95-digit number)

41244166118954044886…14391660210605127681

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

8.248 × 10⁹⁴(95-digit number)

82488332237908089772…28783320421210255359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.248 × 10⁹⁴(95-digit number)

82488332237908089772…28783320421210255361

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

1.649 × 10⁹⁵(96-digit number)

16497666447581617954…57566640842420510719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.649 × 10⁹⁵(96-digit number)

16497666447581617954…57566640842420510721

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

3.299 × 10⁹⁵(96-digit number)

32995332895163235908…15133281684841021439

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 #3,033,101

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