Block #1,120,633

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2015, 7:24:27 AM · Difficulty 10.9358 · 5,687,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f2be41e88ac3b3475995b7a897a5aa660ebb24c575a1bb4f8ff87da37b1191f

View on Chainz ↗

Height

#1,120,633

Difficulty

10.935843

Transactions

Size

14.86 KB

Version

Bits

0aef9361

Nonce

547,813,025

Timestamp

6/21/2015, 7:24:27 AM

Confirmations

5,687,208

Mined by

⛏️ P2SHAM6THobz4jMzDzoneq8e5XveSMvKPVcBG2

Merkle Root

f3e091867e33a2455166e4b122050bd8c4c2c9bb636982063aefe60318ec43d6

Transactions (2)

Coinbase07fd06f9b5bdb3…640b623f3ed4f0

1 in → 1 out8.9100 XPM110 B

AM6THobz…vKPVcBG2

ef00606e7a8e2c…a50c9ae91c59fe

101 in → 2 out2710.0000 XPM14.66 KB

AWkHoi2X…qqC5LjmD ALxjxDeM…LrMd9WZA

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.

1.134 × 10⁹⁷(98-digit number)

11343981843260866704…67483881912374271999

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

1.134 × 10⁹⁷(98-digit number)

11343981843260866704…67483881912374271999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.134 × 10⁹⁷(98-digit number)

11343981843260866704…67483881912374272001

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

2.268 × 10⁹⁷(98-digit number)

22687963686521733408…34967763824748543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.268 × 10⁹⁷(98-digit number)

22687963686521733408…34967763824748544001

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

4.537 × 10⁹⁷(98-digit number)

45375927373043466816…69935527649497087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.537 × 10⁹⁷(98-digit number)

45375927373043466816…69935527649497088001

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

9.075 × 10⁹⁷(98-digit number)

90751854746086933632…39871055298994175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.075 × 10⁹⁷(98-digit number)

90751854746086933632…39871055298994176001

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

1.815 × 10⁹⁸(99-digit number)

18150370949217386726…79742110597988351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.815 × 10⁹⁸(99-digit number)

18150370949217386726…79742110597988352001

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 #1,120,633

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