Home/Chain Registry/Block #772,842

Block #772,842

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/17/2014, 3:13:26 PM · Difficulty 10.9821 · 6,063,603 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fb361eb270dbdb4ebc48a279f473b5697887aa7e2efa4500ca65c10f15e803e

View on Chainz ↗

Height

#772,842

Difficulty

10.982081

Transactions

Size

885 B

Version

Bits

0afb69a5

Nonce

174,673,976

Timestamp

10/17/2014, 3:13:26 PM

Confirmations

6,063,603

Merkle Root

158d85a0ca0e2d634b7b3081cecaa7c95b341899700988681aa2bd2f00db706b

Transactions (4)

Coinbasec7d722fccd1589…9d0a38a27d41f1

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

e29b250c5ec415…0c36507c6dcf9c

1 in → 2 out4.2800 XPM225 B

AMN6qDkt…VuvvTq6f AdDBbcC1…Xina8GKM

3fa4fe0421c493…a61877d279c14c

1 in → 2 out4.2600 XPM225 B

AMyFarm4…6npGvxsv AMrfwgYo…GoE3z7mk

26b345d7eb2f1b…322b9db0638e88

1 in → 2 out4.2600 XPM227 B

AMyFarm4…6npGvxsv AYYAYkHt…qddLtBH3

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.

2.561 × 10⁹⁹(100-digit number)

25617698290648345908…48895015673323520000

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

2.561 × 10⁹⁹(100-digit number)

25617698290648345908…48895015673323519999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.561 × 10⁹⁹(100-digit number)

25617698290648345908…48895015673323520001

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

5.123 × 10⁹⁹(100-digit number)

51235396581296691817…97790031346647039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.123 × 10⁹⁹(100-digit number)

51235396581296691817…97790031346647040001

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

1.024 × 10¹⁰⁰(101-digit number)

10247079316259338363…95580062693294079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.024 × 10¹⁰⁰(101-digit number)

10247079316259338363…95580062693294080001

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

2.049 × 10¹⁰⁰(101-digit number)

20494158632518676727…91160125386588159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.049 × 10¹⁰⁰(101-digit number)

20494158632518676727…91160125386588160001

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

4.098 × 10¹⁰⁰(101-digit number)

40988317265037353454…82320250773176319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.098 × 10¹⁰⁰(101-digit number)

40988317265037353454…82320250773176320001

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

8.197 × 10¹⁰⁰(101-digit number)

81976634530074706908…64640501546352639999

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.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 772842

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 2fb361eb270dbdb4ebc48a279f473b5697887aa7e2efa4500ca65c10f15e803e

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #772,842 on Chainz ↗

Block #772,842

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