Block #842,019

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/6/2014, 7:40:51 AM · Difficulty 10.9739 · 6,000,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f79f8ab2b3fa36c6613ece68af78ec1f10a66ee35d25da65b812b3df1cc9d2ee

View on Chainz ↗

Height

#842,019

Difficulty

10.973884

Transactions

Size

1.01 KB

Version

Bits

0af9506e

Nonce

1,059,896,357

Timestamp

12/6/2014, 7:40:51 AM

Confirmations

6,000,920

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b06a164e30afd7d3ce200a387934ff213bda624fb9145685748d3ae2211ce5b9

Transactions (4)

Coinbase719597138b6c01…de3b8ac4709f61

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

aae91c21ea6adf…ff612625346f2d

2 in → 2 out11.5212 XPM374 B

ANjstiPv…hPdrbeCN AcqLzLhA…eE6LSgnW

99fed303f5b609…df3a4d5a6e0cf6

1 in → 2 out7.1689 XPM227 B

AXKGz6u7…Rb5eth7C AS5SmFfz…DBFm3dks

27bbfb5c33330a…869321ed44f80a

1 in → 2 out7.1853 XPM225 B

ANbP1Nbx…zfVhLfU7 AT49wTzz…Rxy6LPiS

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.

9.093 × 10⁹⁵(96-digit number)

90930086765596826995…44870607020022313679

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

9.093 × 10⁹⁵(96-digit number)

90930086765596826995…44870607020022313679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.093 × 10⁹⁵(96-digit number)

90930086765596826995…44870607020022313681

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

1.818 × 10⁹⁶(97-digit number)

18186017353119365399…89741214040044627359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.818 × 10⁹⁶(97-digit number)

18186017353119365399…89741214040044627361

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

3.637 × 10⁹⁶(97-digit number)

36372034706238730798…79482428080089254719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.637 × 10⁹⁶(97-digit number)

36372034706238730798…79482428080089254721

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

7.274 × 10⁹⁶(97-digit number)

72744069412477461596…58964856160178509439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.274 × 10⁹⁶(97-digit number)

72744069412477461596…58964856160178509441

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

1.454 × 10⁹⁷(98-digit number)

14548813882495492319…17929712320357018879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.454 × 10⁹⁷(98-digit number)

14548813882495492319…17929712320357018881

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

2.909 × 10⁹⁷(98-digit number)

29097627764990984638…35859424640714037759

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 #842,019

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