Block #3,012,645

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2019, 11:21:41 PM · Difficulty 11.1767 · 3,803,778 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c8cca1062290c1662428e2204852d64b383bd93f03b5f6ba03c12203e0d667e2

View on Chainz ↗

Height

#3,012,645

Difficulty

11.176681

Transactions

Size

847 B

Version

Bits

0b2d3afa

Nonce

959,655,127

Timestamp

1/16/2019, 11:21:41 PM

Confirmations

3,803,778

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

f3a619632892f615dbef34e13b7655f51783de38ec6b36bd3d4513137efa2fe3

Transactions (3)

Coinbase1586ab27577e05…255464ce75ee92

1 in → 1 out8.0100 XPM109 B

AbXwmGxD…4XXYP765

f6137c8e59e1f3…481da1a6e9230b

2 in → 2 out15.9600 XPM307 B

ATkwammm…oasHBd7n AaMSJsft…jJcWSbpG

054632fcb7cc3e…fc91d6b851fccd

2 in → 2 out11.8300 XPM341 B

ANSZDoxP…fw9AVB3Z AFspDL7p…6fDLiH6h

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.

1.407 × 10⁹⁴(95-digit number)

14073479262476820405…14071989515922768979

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

1.407 × 10⁹⁴(95-digit number)

14073479262476820405…14071989515922768979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.407 × 10⁹⁴(95-digit number)

14073479262476820405…14071989515922768981

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

2.814 × 10⁹⁴(95-digit number)

28146958524953640810…28143979031845537959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.814 × 10⁹⁴(95-digit number)

28146958524953640810…28143979031845537961

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

5.629 × 10⁹⁴(95-digit number)

56293917049907281620…56287958063691075919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.629 × 10⁹⁴(95-digit number)

56293917049907281620…56287958063691075921

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

1.125 × 10⁹⁵(96-digit number)

11258783409981456324…12575916127382151839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.125 × 10⁹⁵(96-digit number)

11258783409981456324…12575916127382151841

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

2.251 × 10⁹⁵(96-digit number)

22517566819962912648…25151832254764303679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.251 × 10⁹⁵(96-digit number)

22517566819962912648…25151832254764303681

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

4.503 × 10⁹⁵(96-digit number)

45035133639925825296…50303664509528607359

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 #3,012,645

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