Block #2,931,192

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/20/2018, 7:41:33 AM · Difficulty 11.3941 · 3,901,646 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd0014a0a3c2844cef9defc9e903f872f72f59e5d05c6fc56b785a42fbee915b

View on Chainz ↗

Height

#2,931,192

Difficulty

11.394053

Transactions

Size

1.16 KB

Version

Bits

0b64e0ad

Nonce

1,013,788,001

Timestamp

11/20/2018, 7:41:33 AM

Confirmations

3,901,646

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

54ecfa2d8070210ded6e7cc3bfa2f61a53182554a9ed341f4397daad8904f04e

Transactions (4)

Coinbase4979a7d5ec7728…2b1ed223edfe7d

1 in → 1 out7.7200 XPM110 B

AUhjokok…k5m93PZR

8498bd4607a106…4a99d5998e0620

2 in → 2 out15.4300 XPM306 B

Ae9dAN8S…mkaB5aqH AHVzbS1p…rrs5kTcv

19275961ced9ea…edab2e1fb097fe

2 in → 2 out15.4300 XPM307 B

AJWUtVtH…GkrGcrPy AVZY7fRQ…voPLHzeJ

6f3557297d634b…fe30b91f1d0c8d

2 in → 2 out10.8500 XPM374 B

Ae1fWxyX…mDAcevfm AKtg5M5J…UY3VCdzE

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.

1.185 × 10⁹⁷(98-digit number)

11854155837865267426…40412186449001840639

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

1.185 × 10⁹⁷(98-digit number)

11854155837865267426…40412186449001840639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.185 × 10⁹⁷(98-digit number)

11854155837865267426…40412186449001840641

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

2.370 × 10⁹⁷(98-digit number)

23708311675730534853…80824372898003681279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.370 × 10⁹⁷(98-digit number)

23708311675730534853…80824372898003681281

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

4.741 × 10⁹⁷(98-digit number)

47416623351461069706…61648745796007362559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.741 × 10⁹⁷(98-digit number)

47416623351461069706…61648745796007362561

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

9.483 × 10⁹⁷(98-digit number)

94833246702922139413…23297491592014725119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.483 × 10⁹⁷(98-digit number)

94833246702922139413…23297491592014725121

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

1.896 × 10⁹⁸(99-digit number)

18966649340584427882…46594983184029450239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.896 × 10⁹⁸(99-digit number)

18966649340584427882…46594983184029450241

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

3.793 × 10⁹⁸(99-digit number)

37933298681168855765…93189966368058900479

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 #2,931,192

Cookie Preferences