Block #3,011,877

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2019, 10:29:30 AM · Difficulty 11.1772 · 3,821,336 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6733ba748d1da6ca104cf385b0de84dd1e384ea034030d50ead86b9aa364d51f

View on Chainz ↗

Height

#3,011,877

Difficulty

11.177240

Transactions

Size

891 B

Version

Bits

0b2d5f9d

Nonce

670,000,414

Timestamp

1/16/2019, 10:29:30 AM

Confirmations

3,821,336

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

75cd0ed7c80f60241c545c1f90881655ec1791b7b20145ea11baa4724221f9fc

Transactions (4)

Coinbaseae8b54167527be…b801dfa99ba77e

1 in → 1 out8.0200 XPM109 B

AUMQRepm…tAfKmdW1

80917ff8a20929…20f7e24c560e94

2 in → 2 out15.9300 XPM306 B

AbXwmGxD…4XXYP765 AMfZL8Sg…3KgjLnV7

5e03d7b63ad6da…7265232e099693

1 in → 2 out7.9400 XPM192 B

AZsDZAHb…eekmSpib AbXwmGxD…4XXYP765

3f9f829b4261af…ddff01c85a0f8e

1 in → 2 out7.9400 XPM193 B

AKBxhYmY…4XGb9PCf AbXwmGxD…4XXYP765

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.

9.139 × 10⁹⁷(98-digit number)

91395928200455212541…96047453447813857279

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

9.139 × 10⁹⁷(98-digit number)

91395928200455212541…96047453447813857279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.139 × 10⁹⁷(98-digit number)

91395928200455212541…96047453447813857281

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

1.827 × 10⁹⁸(99-digit number)

18279185640091042508…92094906895627714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.827 × 10⁹⁸(99-digit number)

18279185640091042508…92094906895627714561

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

3.655 × 10⁹⁸(99-digit number)

36558371280182085016…84189813791255429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.655 × 10⁹⁸(99-digit number)

36558371280182085016…84189813791255429121

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

7.311 × 10⁹⁸(99-digit number)

73116742560364170033…68379627582510858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.311 × 10⁹⁸(99-digit number)

73116742560364170033…68379627582510858241

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

1.462 × 10⁹⁹(100-digit number)

14623348512072834006…36759255165021716479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.462 × 10⁹⁹(100-digit number)

14623348512072834006…36759255165021716481

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

2.924 × 10⁹⁹(100-digit number)

29246697024145668013…73518510330043432959

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 #3,011,877

Cookie Preferences