Block #2,595,968

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/1/2018, 9:53:09 PM · Difficulty 11.3009 · 4,237,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6da0927fde826060cc61809e250f3a08ed1d26fe2381980b7c3a9f94f2a43d4

View on Chainz ↗

Height

#2,595,968

Difficulty

11.300934

Transactions

Size

720 B

Version

Bits

0b4d0a0b

Nonce

22,240,970

Timestamp

4/1/2018, 9:53:09 PM

Confirmations

4,237,058

Mined by

⛏️ P2SHAHDYmTST9237bftkp2ZTgRCRsWnXFjTd26

Merkle Root

85f00a722463e31f08541e50a48fa0f9e8e024b606ffd8cfd0b0ee2c3c1ff372

Transactions (2)

Coinbase3a8151c88a2e17…2dfe52098da18a

1 in → 1 out7.8300 XPM109 B

AHDYmTST…nXFjTd26

d49feaffe42032…ae2f0242bbee4b

3 in → 2 out20.2529 XPM521 B

AWt5bqzf…v7YQkMGJ AX4VNxJq…JAu6dNwD

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.

5.442 × 10⁹⁵(96-digit number)

54425435746783211831…83221655912104171519

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

5.442 × 10⁹⁵(96-digit number)

54425435746783211831…83221655912104171519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.442 × 10⁹⁵(96-digit number)

54425435746783211831…83221655912104171521

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

1.088 × 10⁹⁶(97-digit number)

10885087149356642366…66443311824208343039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.088 × 10⁹⁶(97-digit number)

10885087149356642366…66443311824208343041

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

2.177 × 10⁹⁶(97-digit number)

21770174298713284732…32886623648416686079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.177 × 10⁹⁶(97-digit number)

21770174298713284732…32886623648416686081

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

4.354 × 10⁹⁶(97-digit number)

43540348597426569464…65773247296833372159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.354 × 10⁹⁶(97-digit number)

43540348597426569464…65773247296833372161

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

8.708 × 10⁹⁶(97-digit number)

87080697194853138929…31546494593666744319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.708 × 10⁹⁶(97-digit number)

87080697194853138929…31546494593666744321

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

1.741 × 10⁹⁷(98-digit number)

17416139438970627785…63092989187333488639

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 #2,595,968

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