Home/Chain Registry/Block #787,705

Block #787,705

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/29/2014, 6:12:25 AM · Difficulty 10.9746 · 6,008,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9355a6da791cbb0652a8b4f899a128689cf49f337daefd08c55bdf1825756cf6

View on Chainz ↗

Height

#787,705

Difficulty

10.974565

Transactions

Size

10.99 KB

Version

Bits

0af97d1d

Nonce

1,954,379,225

Timestamp

10/29/2014, 6:12:25 AM

Confirmations

6,008,927

Merkle Root

a931e54b7d65d365d506e2ce02f9235dc5dada0a9bedc9962a7a050878adf612

Transactions (4)

Coinbase0ccb285fea689a…103ffffb4b550a

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

42db19bd51c819…ef86fe36dcd478

71 in → 2 out50000.0100 XPM10.34 KB

ATNFg4tq…AMdaKJFH AMdxbmJh…krUodykA

7073325200a269…c564a932e3a00f

1 in → 2 out8.2700 XPM227 B

ALXznLsu…WY8fnzBJ AGdWVjRk…LFVsqCnK

db52fb23a9e951…2438ab61942b85

1 in → 2 out7.5963 XPM226 B

AGakFRvu…DuppRaTS AGEed55R…9o5EJWws

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.

8.816 × 10⁹⁶(97-digit number)

88164563984019685771…02096584675232583680

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

8.816 × 10⁹⁶(97-digit number)

88164563984019685771…02096584675232583679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.816 × 10⁹⁶(97-digit number)

88164563984019685771…02096584675232583681

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

1.763 × 10⁹⁷(98-digit number)

17632912796803937154…04193169350465167359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.763 × 10⁹⁷(98-digit number)

17632912796803937154…04193169350465167361

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

3.526 × 10⁹⁷(98-digit number)

35265825593607874308…08386338700930334719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.526 × 10⁹⁷(98-digit number)

35265825593607874308…08386338700930334721

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

7.053 × 10⁹⁷(98-digit number)

70531651187215748617…16772677401860669439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.053 × 10⁹⁷(98-digit number)

70531651187215748617…16772677401860669441

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

1.410 × 10⁹⁸(99-digit number)

14106330237443149723…33545354803721338879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.410 × 10⁹⁸(99-digit number)

14106330237443149723…33545354803721338881

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

2.821 × 10⁹⁸(99-digit number)

28212660474886299446…67090709607442677759

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 787705

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 9355a6da791cbb0652a8b4f899a128689cf49f337daefd08c55bdf1825756cf6

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 #787,705 on Chainz ↗