Block #2,583,444

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/24/2018, 7:07:50 PM · Difficulty 11.1737 · 4,259,857 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

52d55cb4c988dac4c473a315268f2a4246faf4534786f771147db780b61efe67

View on Chainz ↗

Height

#2,583,444

Difficulty

11.173651

Transactions

Size

1.41 KB

Version

Bits

0b2c745d

Nonce

1,814,998,606

Timestamp

3/24/2018, 7:07:50 PM

Confirmations

4,259,857

Mined by

⛏️ P2SHAM2cRmFeKSZrryiatqnoKRicMBCyQS4WPB

Merkle Root

09a22f036b1f60ceb7bd6270f2e7911129d0788f938811c9a7dc04df53fcf8a2

Transactions (3)

Coinbase471c1cc85d712b…55fcc5e48a3939

1 in → 1 out8.0200 XPM110 B

AM2cRmFe…CyQS4WPB

fdbb165b971f87…4e248d9161e7f6

2 in → 2 out16.3900 XPM306 B

AGAvUT2N…SytLXZkj AW3QZZmg…j2rGjUkp

98e28bd9467795…3adcf813a203ec

6 in → 1 out10.0000 XPM933 B

AUkRFULb…4wHt2veo

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.

8.483 × 10⁹³(94-digit number)

84838643530187053105…49629785798866734809

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

8.483 × 10⁹³(94-digit number)

84838643530187053105…49629785798866734809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.483 × 10⁹³(94-digit number)

84838643530187053105…49629785798866734811

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

1.696 × 10⁹⁴(95-digit number)

16967728706037410621…99259571597733469619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.696 × 10⁹⁴(95-digit number)

16967728706037410621…99259571597733469621

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

3.393 × 10⁹⁴(95-digit number)

33935457412074821242…98519143195466939239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.393 × 10⁹⁴(95-digit number)

33935457412074821242…98519143195466939241

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

6.787 × 10⁹⁴(95-digit number)

67870914824149642484…97038286390933878479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.787 × 10⁹⁴(95-digit number)

67870914824149642484…97038286390933878481

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

1.357 × 10⁹⁵(96-digit number)

13574182964829928496…94076572781867756959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.357 × 10⁹⁵(96-digit number)

13574182964829928496…94076572781867756961

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

2.714 × 10⁹⁵(96-digit number)

27148365929659856993…88153145563735513919

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 #2,583,444

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