Block #2,165,325

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2017, 2:47:15 AM · Difficulty 10.8983 · 4,674,940 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49565b52a4faf8217b0ae68ccf5d04cbaacee28367c8851ddf4e6b82a8432056

View on Chainz ↗

Height

#2,165,325

Difficulty

10.898254

Transactions

Size

1.22 KB

Version

Bits

0ae5f3f1

Nonce

1,059,615,471

Timestamp

6/18/2017, 2:47:15 AM

Confirmations

4,674,940

Mined by

⛏️ P2SHAb6LQEcQAcQmLtcpZ5sGYhL2xNVpe9FJ5U

Merkle Root

f137d4cd2002b233a3fde79b8a911827ad0ac5a95ed346bb2f0d32109f3be859

Transactions (3)

Coinbasea2284f63178db9…c6450c479b8295

1 in → 1 out8.4300 XPM110 B

Ab6LQEcQ…Vpe9FJ5U

39ae6fdff5905b…779aaa075f69db

5 in → 2 out300.0100 XPM820 B

AT7oJ6p3…4VxESh9u AYJCQHHj…bPaKNbHS

5df30400c7c634…58dd6fa75bc73f

1 in → 2 out6.3357 XPM226 B

APvejb7z…o53FnC97 ANP9Msm5…tnnC3N8T

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.

6.677 × 10⁹⁴(95-digit number)

66773118722871516621…79037203214139535079

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

6.677 × 10⁹⁴(95-digit number)

66773118722871516621…79037203214139535079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.677 × 10⁹⁴(95-digit number)

66773118722871516621…79037203214139535081

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

1.335 × 10⁹⁵(96-digit number)

13354623744574303324…58074406428279070159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.335 × 10⁹⁵(96-digit number)

13354623744574303324…58074406428279070161

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

2.670 × 10⁹⁵(96-digit number)

26709247489148606648…16148812856558140319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.670 × 10⁹⁵(96-digit number)

26709247489148606648…16148812856558140321

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

5.341 × 10⁹⁵(96-digit number)

53418494978297213297…32297625713116280639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.341 × 10⁹⁵(96-digit number)

53418494978297213297…32297625713116280641

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

1.068 × 10⁹⁶(97-digit number)

10683698995659442659…64595251426232561279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.068 × 10⁹⁶(97-digit number)

10683698995659442659…64595251426232561281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,165,325

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