Block #3,011,736

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2019, 8:17:18 AM · Difficulty 11.1767 · 3,827,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fdaaa8bc421f3340d83ccf8d9065f572df36fac44ac40ee74ab0cce3edaa2b3

View on Chainz ↗

Height

#3,011,736

Difficulty

11.176744

Transactions

Size

1.64 KB

Version

Bits

0b2d3f20

Nonce

144,173,155

Timestamp

1/16/2019, 8:17:18 AM

Confirmations

3,827,994

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

066d8a144df65c741f8fd424f904a0c8669303b7053c708f1143016d53869bd6

Transactions (5)

Coinbased570f475fdfa84…737069b552fb42

1 in → 1 out8.0300 XPM110 B

AbXwmGxD…4XXYP765

c39c71d534136c…f1b3546aa03e38

2 in → 2 out15.9300 XPM306 B

APVKWthF…PMMxwRoz AaCC148s…ofcS8xkb

119e07f6cd28c1…5687a9fe51076f

2 in → 2 out15.9100 XPM306 B

ANGy9bbA…xMyvvQEg AW5MCQAK…xrFqXeRe

dfb41b04ef83e6…36713f30eff969

2 in → 2 out13.9400 XPM341 B

AXu7F5Qm…JYZt5QLG Aeb1d5GJ…SXdKc84K

f7ad5f101ba1ce…ccbc99f2c54a68

3 in → 2 out10.6400 XPM523 B

AaHsEQd6…A22sKQ7o ALkTQMLU…k4UgGFcB

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.

2.538 × 10⁹⁸(99-digit number)

25387896420144056177…53127023416497766399

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

2.538 × 10⁹⁸(99-digit number)

25387896420144056177…53127023416497766399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.538 × 10⁹⁸(99-digit number)

25387896420144056177…53127023416497766401

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

5.077 × 10⁹⁸(99-digit number)

50775792840288112355…06254046832995532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.077 × 10⁹⁸(99-digit number)

50775792840288112355…06254046832995532801

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

1.015 × 10⁹⁹(100-digit number)

10155158568057622471…12508093665991065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.015 × 10⁹⁹(100-digit number)

10155158568057622471…12508093665991065601

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

2.031 × 10⁹⁹(100-digit number)

20310317136115244942…25016187331982131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.031 × 10⁹⁹(100-digit number)

20310317136115244942…25016187331982131201

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

4.062 × 10⁹⁹(100-digit number)

40620634272230489884…50032374663964262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.062 × 10⁹⁹(100-digit number)

40620634272230489884…50032374663964262401

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

8.124 × 10⁹⁹(100-digit number)

81241268544460979769…00064749327928524799

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 #3,011,736

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