Block #3,045,629

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/9/2019, 1:59:33 PM · Difficulty 10.9961 · 3,797,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c91fe8194b4227a7c388ba72b49a74aeaf7c208fb9b950f5b1bd71f393bad7a6

View on Chainz ↗

Height

#3,045,629

Difficulty

10.996081

Transactions

Size

722 B

Version

Bits

0afeff2c

Nonce

650,183,138

Timestamp

2/9/2019, 1:59:33 PM

Confirmations

3,797,368

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

a0471ca975600f084a9693e2bc04032b58c802413dbf505875b379711bb10ae2

Transactions (2)

Coinbasef135b386350796…02a435e63def1c

1 in → 1 out8.2700 XPM109 B

AbXwmGxD…4XXYP765

33df1ac5c84c10…0bc8e1c23e2b32

3 in → 2 out20.9588 XPM523 B

AG4SoT23…CTS3g2RN AXgtGpgA…JHaMAU9B

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.

2.647 × 10⁹⁵(96-digit number)

26477745006925593208…31299366076775658399

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

2.647 × 10⁹⁵(96-digit number)

26477745006925593208…31299366076775658399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.647 × 10⁹⁵(96-digit number)

26477745006925593208…31299366076775658401

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

5.295 × 10⁹⁵(96-digit number)

52955490013851186417…62598732153551316799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.295 × 10⁹⁵(96-digit number)

52955490013851186417…62598732153551316801

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

1.059 × 10⁹⁶(97-digit number)

10591098002770237283…25197464307102633599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.059 × 10⁹⁶(97-digit number)

10591098002770237283…25197464307102633601

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

2.118 × 10⁹⁶(97-digit number)

21182196005540474567…50394928614205267199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.118 × 10⁹⁶(97-digit number)

21182196005540474567…50394928614205267201

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

4.236 × 10⁹⁶(97-digit number)

42364392011080949134…00789857228410534399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.236 × 10⁹⁶(97-digit number)

42364392011080949134…00789857228410534401

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

8.472 × 10⁹⁶(97-digit number)

84728784022161898268…01579714456821068799

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 #3,045,629

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