Block #2,311,905

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/27/2017, 9:40:10 PM · Difficulty 10.9064 · 4,529,489 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f4cd02c37fa44f2aaf80f71c735462ce0cbf30c4bf21cb258638b11b5637fba

View on Chainz ↗

Height

#2,311,905

Difficulty

10.906387

Transactions

Size

2.96 KB

Version

Bits

0ae80900

Nonce

70,880,984

Timestamp

9/27/2017, 9:40:10 PM

Confirmations

4,529,489

Mined by

⛏️ P2SHALoNYgu7T4ZAdwb6312Nyc9Eu7VJmUQgWs

Merkle Root

0b3f1393fced953cfc1ac0960b8f2084b6c04d8251ff02fb4701c9ada27d1a26

Transactions (5)

Coinbase7c7b5077d62ef1…971957526cbcbb

1 in → 1 out8.4400 XPM110 B

ALoNYgu7…VJmUQgWs

75e8f60880b0c9…d9f9fc7ec34264

10 in → 2 out0.5100 XPM1.52 KB

AeAnM7H7…VeyU2Jn6 ASiSiXEG…j9XRmfr1

bdf38fe5059bf3…671ff88c6151c2

2 in → 2 out4.7823 XPM374 B

AK7Cx3BJ…HpxiXzZP AaaYoKho…cUUmc4Tj

88471e2628e841…cc4fb344acda72

1 in → 2 out1.8369 XPM226 B

AHxbbDcP…irfdjnVy AQBd5saN…gzPybU6u

74ed178c77ad82…68555234af44ce

4 in → 2 out4.2262 XPM670 B

AZLPmJvs…pDWmzqwB AYXNENHJ…x6HvxHXe

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.

2.405 × 10⁹⁵(96-digit number)

24054239658913221323…83387669268488929919

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

2.405 × 10⁹⁵(96-digit number)

24054239658913221323…83387669268488929919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.405 × 10⁹⁵(96-digit number)

24054239658913221323…83387669268488929921

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

4.810 × 10⁹⁵(96-digit number)

48108479317826442647…66775338536977859839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.810 × 10⁹⁵(96-digit number)

48108479317826442647…66775338536977859841

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

9.621 × 10⁹⁵(96-digit number)

96216958635652885294…33550677073955719679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.621 × 10⁹⁵(96-digit number)

96216958635652885294…33550677073955719681

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

1.924 × 10⁹⁶(97-digit number)

19243391727130577058…67101354147911439359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.924 × 10⁹⁶(97-digit number)

19243391727130577058…67101354147911439361

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

3.848 × 10⁹⁶(97-digit number)

38486783454261154117…34202708295822878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.848 × 10⁹⁶(97-digit number)

38486783454261154117…34202708295822878721

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 #2,311,905

Cookie Preferences