Block #3,011,911

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2019, 11:03:44 AM · Difficulty 11.1775 · 3,804,118 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb03053fd34715250db2ca2ecfb30da081287511b7e945687003f37d0ac7ec2d

View on Chainz ↗

Height

#3,011,911

Difficulty

11.177497

Transactions

Size

1.16 KB

Version

Bits

0b2d7073

Nonce

563,211,791

Timestamp

1/16/2019, 11:03:44 AM

Confirmations

3,804,118

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

883d3e2c0a351c22b3e306f676d42bd8ab9480fb8f196aba682388abd466d784

Transactions (4)

Coinbase176b3d0a6687dc…5a9e4d2538ff9b

1 in → 1 out8.0200 XPM110 B

AbXwmGxD…4XXYP765

25b87a1eb56dbd…b6b007b51e47db

2 in → 2 out15.9300 XPM307 B

ANiRSGwW…LtXULkMk APj3mTvV…yS4aDESL

3dedba74be0a34…37bf3c6ebda783

2 in → 2 out15.8900 XPM306 B

AFspDL7p…6fDLiH6h AGsZ3UhF…qdtnLT5W

9dd81a195b9909…11a12dd0e961b5

2 in → 2 out11.8100 XPM375 B

ARh926hd…WYcLM5kw AdipemGE…2BpWEdh4

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.

2.899 × 10⁹⁸(99-digit number)

28993249230793626005…10255051951411363839

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

2.899 × 10⁹⁸(99-digit number)

28993249230793626005…10255051951411363839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.899 × 10⁹⁸(99-digit number)

28993249230793626005…10255051951411363841

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

5.798 × 10⁹⁸(99-digit number)

57986498461587252010…20510103902822727679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.798 × 10⁹⁸(99-digit number)

57986498461587252010…20510103902822727681

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

1.159 × 10⁹⁹(100-digit number)

11597299692317450402…41020207805645455359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.159 × 10⁹⁹(100-digit number)

11597299692317450402…41020207805645455361

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

2.319 × 10⁹⁹(100-digit number)

23194599384634900804…82040415611290910719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.319 × 10⁹⁹(100-digit number)

23194599384634900804…82040415611290910721

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

4.638 × 10⁹⁹(100-digit number)

46389198769269801608…64080831222581821439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.638 × 10⁹⁹(100-digit number)

46389198769269801608…64080831222581821441

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

9.277 × 10⁹⁹(100-digit number)

92778397538539603216…28161662445163642879

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 #3,011,911

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