Block #2,260,911

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/21/2017, 1:45:49 AM · Difficulty 10.9516 · 4,565,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c8446158e64827398fc6d3b8eb4eaf41ade93f27cd4c43c845be3874980679e

View on Chainz ↗

Height

#2,260,911

Difficulty

10.951648

Transactions

Size

1.57 KB

Version

Bits

0af39f33

Nonce

34,193,367

Timestamp

8/21/2017, 1:45:49 AM

Confirmations

4,565,930

Mined by

⛏️ P2SHAVE1HJQpYCyB15DuCsK41VoRsnK3hfbD3m

Merkle Root

c7f3b17c6a3e2ab16a2af4425fcce7bc7bae71ef86d45b9aebde1cc2fb4712dd

Transactions (2)

Coinbasefbc2d0dcc0833f…630af784210a37

1 in → 1 out8.3400 XPM109 B

AVE1HJQp…K3hfbD3m

a1afb807dc9cbe…c7c068fb833af3

9 in → 2 out1210.5462 XPM1.37 KB

ALzjZAgs…AKEUP9SR AZwTvsn8…MYtMhxUx

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.

9.838 × 10⁹⁴(95-digit number)

98384430406156945051…17222088798568263679

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

9.838 × 10⁹⁴(95-digit number)

98384430406156945051…17222088798568263679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.838 × 10⁹⁴(95-digit number)

98384430406156945051…17222088798568263681

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

1.967 × 10⁹⁵(96-digit number)

19676886081231389010…34444177597136527359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.967 × 10⁹⁵(96-digit number)

19676886081231389010…34444177597136527361

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

3.935 × 10⁹⁵(96-digit number)

39353772162462778020…68888355194273054719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.935 × 10⁹⁵(96-digit number)

39353772162462778020…68888355194273054721

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

7.870 × 10⁹⁵(96-digit number)

78707544324925556041…37776710388546109439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.870 × 10⁹⁵(96-digit number)

78707544324925556041…37776710388546109441

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

1.574 × 10⁹⁶(97-digit number)

15741508864985111208…75553420777092218879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.574 × 10⁹⁶(97-digit number)

15741508864985111208…75553420777092218881

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

3.148 × 10⁹⁶(97-digit number)

31483017729970222416…51106841554184437759

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 #2,260,911

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