Block #2,589,027

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/27/2018, 10:55:35 PM · Difficulty 11.3273 · 4,252,912 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b100dd3ab7a1a89395c284ed8c305b01bcf26f484ca9ca2504b6ce03b77cd1f2

View on Chainz ↗

Height

#2,589,027

Difficulty

11.327304

Transactions

Size

1.13 KB

Version

Bits

0b53ca36

Nonce

193,955,548

Timestamp

3/27/2018, 10:55:35 PM

Confirmations

4,252,912

Mined by

⛏️ P2SHALgxZkqUsDVVp1kiC5LAyckQipiBf3BX7T

Merkle Root

6bf67b7b37c9decbf2217d78eb0d14f9d446d5ca58c16d9586be7c22dd9919e3

Transactions (4)

Coinbase4a5fc246c3df2f…4c7b8afb019b8a

1 in → 1 out7.8100 XPM109 B

ALgxZkqU…iBf3BX7T

e825a053d3ceed…9acdecbcb4f974

2 in → 2 out15.7300 XPM306 B

AcH8TQdi…KHbRe4MX AR3cBEuE…9vc8keub

459a9f55471123…019df1919b5a55

2 in → 2 out15.7300 XPM307 B

AW3QZZmg…j2rGjUkp Abaft3P8…9FCooLXj

bcd73858266382…5257878f09b1d1

2 in → 2 out13.5900 XPM340 B

AHSWpUrB…aKSHiDiv ANGC5cU8…U2owYeyC

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.

7.770 × 10⁹⁶(97-digit number)

77705268363599519251…83182823386969077759

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

7.770 × 10⁹⁶(97-digit number)

77705268363599519251…83182823386969077759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.770 × 10⁹⁶(97-digit number)

77705268363599519251…83182823386969077761

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

1.554 × 10⁹⁷(98-digit number)

15541053672719903850…66365646773938155519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.554 × 10⁹⁷(98-digit number)

15541053672719903850…66365646773938155521

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

3.108 × 10⁹⁷(98-digit number)

31082107345439807700…32731293547876311039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.108 × 10⁹⁷(98-digit number)

31082107345439807700…32731293547876311041

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

6.216 × 10⁹⁷(98-digit number)

62164214690879615401…65462587095752622079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.216 × 10⁹⁷(98-digit number)

62164214690879615401…65462587095752622081

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

1.243 × 10⁹⁸(99-digit number)

12432842938175923080…30925174191505244159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.243 × 10⁹⁸(99-digit number)

12432842938175923080…30925174191505244161

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

2.486 × 10⁹⁸(99-digit number)

24865685876351846160…61850348383010488319

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 #2,589,027

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