Block #3,004,583

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/11/2019, 6:06:31 AM · Difficulty 11.2043 · 3,829,033 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bd56d0543c0caae77cb5ca55545f14f4b37dbb3d32d32fcc1f86c43c78469d2

View on Chainz ↗

Height

#3,004,583

Difficulty

11.204314

Transactions

Size

1.31 KB

Version

Bits

0b344df2

Nonce

560,897,437

Timestamp

1/11/2019, 6:06:31 AM

Confirmations

3,829,033

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

15197f8c1bbacb29bf137eefb19282326a8d2b14a724da699fcb41ecc5dedf75

Transactions (3)

Coinbase244c416e03b9e3…38914f525d6bd0

1 in → 1 out7.9700 XPM110 B

AUhjokok…k5m93PZR

b621e2a777254e…d2e6f886a04405

7 in → 2 out50.6121 XPM910 B

AbXwmGxD…4XXYP765 ALdXNNLi…KbXoShEJ

62a2800f58b552…e1e33158746ab2

1 in → 2 out5.4289 XPM226 B

AbXwmGxD…4XXYP765 AYUY6QBZ…nstBEWCQ

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.

1.558 × 10⁹⁷(98-digit number)

15585323364472265467…29428003020836837759

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

1.558 × 10⁹⁷(98-digit number)

15585323364472265467…29428003020836837759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.558 × 10⁹⁷(98-digit number)

15585323364472265467…29428003020836837761

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

3.117 × 10⁹⁷(98-digit number)

31170646728944530935…58856006041673675519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.117 × 10⁹⁷(98-digit number)

31170646728944530935…58856006041673675521

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

6.234 × 10⁹⁷(98-digit number)

62341293457889061870…17712012083347351039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.234 × 10⁹⁷(98-digit number)

62341293457889061870…17712012083347351041

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

1.246 × 10⁹⁸(99-digit number)

12468258691577812374…35424024166694702079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.246 × 10⁹⁸(99-digit number)

12468258691577812374…35424024166694702081

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

2.493 × 10⁹⁸(99-digit number)

24936517383155624748…70848048333389404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.493 × 10⁹⁸(99-digit number)

24936517383155624748…70848048333389404161

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

4.987 × 10⁹⁸(99-digit number)

49873034766311249496…41696096666778808319

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 #3,004,583

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