Home/Chain Registry/Block #211,221

Block #211,221

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 2:36:04 PM · Difficulty 9.9151 · 6,580,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df4d0845b82e02aa0d3c18c277ff17caf3e5131c1989966f3cb38ba80a0caff9

View on Chainz ↗

Height

#211,221

Difficulty

9.915144

Transactions

Size

207 B

Version

Bits

09ea46e8

Nonce

83,886,884

Timestamp

10/15/2013, 2:36:04 PM

Confirmations

6,580,517

Merkle Root

83eca598d37d92a965cea915317ba1c3f1f66626473af34195cb9177ef994362

Transactions (1)

Coinbase83eca598d37d92…cb9177ef994362

1 in → 1 out10.1600 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.

1.515 × 10⁹⁶(97-digit number)

15151379588034546054…65845469550292675400

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

1.515 × 10⁹⁶(97-digit number)

15151379588034546054…65845469550292675399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.515 × 10⁹⁶(97-digit number)

15151379588034546054…65845469550292675401

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

3.030 × 10⁹⁶(97-digit number)

30302759176069092109…31690939100585350799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.030 × 10⁹⁶(97-digit number)

30302759176069092109…31690939100585350801

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

6.060 × 10⁹⁶(97-digit number)

60605518352138184219…63381878201170701599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.060 × 10⁹⁶(97-digit number)

60605518352138184219…63381878201170701601

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

1.212 × 10⁹⁷(98-digit number)

12121103670427636843…26763756402341403199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.212 × 10⁹⁷(98-digit number)

12121103670427636843…26763756402341403201

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

2.424 × 10⁹⁷(98-digit number)

24242207340855273687…53527512804682806399

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 211221

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 df4d0845b82e02aa0d3c18c277ff17caf3e5131c1989966f3cb38ba80a0caff9

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 #211,221 on Chainz ↗