Home/Chain Registry/Block #221,965

Block #221,965

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 9:30:16 PM · Difficulty 9.9399 · 6,569,125 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dad6b6fa431de104f0f357a91beb6eb14fa8fcfc306aae76fed0a66c541e81a8

View on Chainz ↗

Height

#221,965

Difficulty

9.939868

Transactions

Size

209 B

Version

Bits

09f09b2f

Nonce

67,109,298

Timestamp

10/21/2013, 9:30:16 PM

Confirmations

6,569,125

Merkle Root

e5d23a18eb4b1a36579f1bba51209a2a0ff1509214f3641307f06a16fac4433a

Transactions (1)

Coinbasee5d23a18eb4b1a…f06a16fac4433a

1 in → 1 out10.1100 XPM116 B

AcLBm5Z9…S683d7c3

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.

3.579 × 10¹⁰¹(102-digit number)

35797475160552220903…44091072715886233600

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

3.579 × 10¹⁰¹(102-digit number)

35797475160552220903…44091072715886233599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.579 × 10¹⁰¹(102-digit number)

35797475160552220903…44091072715886233601

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

7.159 × 10¹⁰¹(102-digit number)

71594950321104441807…88182145431772467199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.159 × 10¹⁰¹(102-digit number)

71594950321104441807…88182145431772467201

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

1.431 × 10¹⁰²(103-digit number)

14318990064220888361…76364290863544934399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.431 × 10¹⁰²(103-digit number)

14318990064220888361…76364290863544934401

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

2.863 × 10¹⁰²(103-digit number)

28637980128441776723…52728581727089868799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.863 × 10¹⁰²(103-digit number)

28637980128441776723…52728581727089868801

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

5.727 × 10¹⁰²(103-digit number)

57275960256883553446…05457163454179737599

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 221965

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 dad6b6fa431de104f0f357a91beb6eb14fa8fcfc306aae76fed0a66c541e81a8

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 #221,965 on Chainz ↗