Block #2,140,092

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/1/2017, 5:51:20 AM · Difficulty 10.8766 · 4,702,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

893c5cda7b2d256ff3cd38fa23687306635fd6abb8f26ef70bd2da8192a7cc5a

View on Chainz ↗

Height

#2,140,092

Difficulty

10.876619

Transactions

Size

1.96 KB

Version

Bits

0ae06a1b

Nonce

1,175,182,834

Timestamp

6/1/2017, 5:51:20 AM

Confirmations

4,702,211

Mined by

⛏️ P2SHATEbbwZVqzPgu39J78pfy7VAMiTHwyTDMU

Merkle Root

49a5e10530b37cdf22e3610e8ddd26eb3a9fde39497989eedfafc02b5553161a

Transactions (5)

Coinbasef3eeaca4ba529b…344fc05a9f31c8

1 in → 1 out8.5300 XPM109 B

ATEbbwZV…THwyTDMU

06208f8e4683ed…e84ee8bc27bd41

5 in → 2 out39.8448 XPM817 B

AYAuRWxY…Rg3t4M63 ASVqYud8…zAtx2Ynv

e6af113f96a33e…665dd2899d55ae

2 in → 2 out16.8300 XPM305 B

AN83v1TU…kcXerDsJ AQ7YrZV9…gqKLot6d

819ba1942c6f38…77ba220d5275a6

2 in → 2 out16.8300 XPM308 B

AHbyumek…ry7WXVsp AMRtYs4p…FoiMgrBf

aefe070be89b76…fcc57e37de4e90

2 in → 2 out6.6873 XPM374 B

ASdXKexa…kch59HW5 ANTPDHQv…yDRBFVHQ

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.

1.102 × 10⁹⁸(99-digit number)

11021444471363535992…64589660764760063999

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

1.102 × 10⁹⁸(99-digit number)

11021444471363535992…64589660764760063999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.102 × 10⁹⁸(99-digit number)

11021444471363535992…64589660764760064001

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

2.204 × 10⁹⁸(99-digit number)

22042888942727071984…29179321529520127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.204 × 10⁹⁸(99-digit number)

22042888942727071984…29179321529520128001

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

4.408 × 10⁹⁸(99-digit number)

44085777885454143969…58358643059040255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.408 × 10⁹⁸(99-digit number)

44085777885454143969…58358643059040256001

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

8.817 × 10⁹⁸(99-digit number)

88171555770908287938…16717286118080511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.817 × 10⁹⁸(99-digit number)

88171555770908287938…16717286118080512001

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

1.763 × 10⁹⁹(100-digit number)

17634311154181657587…33434572236161023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.763 × 10⁹⁹(100-digit number)

17634311154181657587…33434572236161024001

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

3.526 × 10⁹⁹(100-digit number)

35268622308363315175…66869144472322047999

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 #2,140,092

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