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Block #121,234

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/17/2013, 4:52:28 PM · Difficulty 9.7521 · 6,675,151 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b2ce6f37ed1f2e034a5791ec971bfbc1344e2134c83dd02850f37cb5eba422f

View on Chainz ↗

Height

#121,234

Difficulty

9.752124

Transactions

Size

724 B

Version

Bits

09c08b2d

Nonce

75,931

Timestamp

8/17/2013, 4:52:28 PM

Confirmations

6,675,151

Merkle Root

a0a6c50354a41f8cb5a58eb592c715a6b1d925eafe142945f160fff0c9493487

Transactions (2)

Coinbase4320147f1aaeae…e0b1b4ff22cc31

1 in → 1 out10.5100 XPM109 B

Ac6zLb3z…GoH5guHt

f1a646f2bb0598…90091df6adc541

3 in → 2 out83.6397 XPM522 B

AS5CU7Fd…PgsZPYm8 AcWNpkXk…cRTM3N8y

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.

1.052 × 10¹⁰¹(102-digit number)

10524358137463455235…13347679298899203190

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

1.052 × 10¹⁰¹(102-digit number)

10524358137463455235…13347679298899203189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.052 × 10¹⁰¹(102-digit number)

10524358137463455235…13347679298899203191

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

2.104 × 10¹⁰¹(102-digit number)

21048716274926910470…26695358597798406379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.104 × 10¹⁰¹(102-digit number)

21048716274926910470…26695358597798406381

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

4.209 × 10¹⁰¹(102-digit number)

42097432549853820941…53390717195596812759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.209 × 10¹⁰¹(102-digit number)

42097432549853820941…53390717195596812761

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

8.419 × 10¹⁰¹(102-digit number)

84194865099707641882…06781434391193625519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.419 × 10¹⁰¹(102-digit number)

84194865099707641882…06781434391193625521

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

1.683 × 10¹⁰²(103-digit number)

16838973019941528376…13562868782387251039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.683 × 10¹⁰²(103-digit number)

16838973019941528376…13562868782387251041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 121234

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 7b2ce6f37ed1f2e034a5791ec971bfbc1344e2134c83dd02850f37cb5eba422f

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 #121,234 on Chainz ↗