Home/Chain Registry/Block #122,513

Block #122,513

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 1:04:54 PM · Difficulty 9.7557 · 6,679,352 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8567016953a926c776c4abc1459ffe8e7282d2861439bcee94b790224fe01a92

View on Chainz ↗

Height

#122,513

Difficulty

9.755728

Transactions

Size

709 B

Version

Bits

09c1775f

Nonce

256,336

Timestamp

8/18/2013, 1:04:54 PM

Confirmations

6,679,352

Merkle Root

c26ad1d37490e1bd2f6d6d307c83c7f8de9d2836ffcbea5a6c4affc972eb5907

Transactions (4)

Coinbase0a096d74ef4d5d…d22fa4876ac59c

1 in → 1 out10.5282 XPM109 B

ATcJ5D2p…22sPFnAE

951e9db427d7ac…e99b060ca03866

1 in → 1 out10.5000 XPM158 B

AaTaKq6N…LUemjxyC

a83fb2ff008a10…0eee92f864de0a

1 in → 1 out10.5000 XPM158 B

AZjAawhu…JwrCuhga

30fc3345c2a9c5…6beaa3d21f78c5

1 in → 1 out3.4500 XPM192 B

ARTVKKSR…2MFWruti

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.

1.413 × 10⁹⁹(100-digit number)

14136109553171156572…07646336599150067300

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

1.413 × 10⁹⁹(100-digit number)

14136109553171156572…07646336599150067299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.413 × 10⁹⁹(100-digit number)

14136109553171156572…07646336599150067301

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

2.827 × 10⁹⁹(100-digit number)

28272219106342313145…15292673198300134599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.827 × 10⁹⁹(100-digit number)

28272219106342313145…15292673198300134601

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

5.654 × 10⁹⁹(100-digit number)

56544438212684626291…30585346396600269199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.654 × 10⁹⁹(100-digit number)

56544438212684626291…30585346396600269201

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

1.130 × 10¹⁰⁰(101-digit number)

11308887642536925258…61170692793200538399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.130 × 10¹⁰⁰(101-digit number)

11308887642536925258…61170692793200538401

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

2.261 × 10¹⁰⁰(101-digit number)

22617775285073850516…22341385586401076799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 122513

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 8567016953a926c776c4abc1459ffe8e7282d2861439bcee94b790224fe01a92

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 #122,513 on Chainz ↗