Block #2,943,132

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/28/2018, 2:40:50 PM · Difficulty 11.3944 · 3,893,845 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e2736cb06bbdb765c4cba0798820e6aba91549da1845b232e43d3a009390472

View on Chainz ↗

Height

#2,943,132

Difficulty

11.394366

Transactions

Size

607 B

Version

Bits

0b64f532

Nonce

249,989,389

Timestamp

11/28/2018, 2:40:50 PM

Confirmations

3,893,845

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

ad9160d7862c76703db92593d9a1da6a10c6747c8c6394be8853aa53ba754ddf

Transactions (2)

Coinbase54b2e48471281c…c791093e2722b8

1 in → 1 out7.7000 XPM110 B

AUhjokok…k5m93PZR

6ab726ef8f1c26…d6337941f6622f

2 in → 3 out200.0101 XPM407 B

AJmygDFY…A7mV6JpZ AUKMSzWk…YE7xmxq8 Ae4Vnvpq…dje5Qcjz

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.

1.720 × 10⁹⁴(95-digit number)

17209094064681915236…05479656975616059839

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

1.720 × 10⁹⁴(95-digit number)

17209094064681915236…05479656975616059839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.720 × 10⁹⁴(95-digit number)

17209094064681915236…05479656975616059841

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

3.441 × 10⁹⁴(95-digit number)

34418188129363830472…10959313951232119679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.441 × 10⁹⁴(95-digit number)

34418188129363830472…10959313951232119681

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

6.883 × 10⁹⁴(95-digit number)

68836376258727660945…21918627902464239359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.883 × 10⁹⁴(95-digit number)

68836376258727660945…21918627902464239361

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

1.376 × 10⁹⁵(96-digit number)

13767275251745532189…43837255804928478719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.376 × 10⁹⁵(96-digit number)

13767275251745532189…43837255804928478721

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

2.753 × 10⁹⁵(96-digit number)

27534550503491064378…87674511609856957439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.753 × 10⁹⁵(96-digit number)

27534550503491064378…87674511609856957441

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

5.506 × 10⁹⁵(96-digit number)

55069101006982128756…75349023219713914879

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 #2,943,132

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