Home/Chain Registry/Block #60,269

Block #60,269

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 7:02:01 AM · Difficulty 8.9685 · 6,729,592 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6fd238e01f47e09f86943c13a50f8ecfbc2ea35ca8bd31581f100cd4cf063b6

View on Chainz ↗

Height

#60,269

Difficulty

8.968510

Transactions

Size

204 B

Version

Bits

08f7f04b

Nonce

1,164

Timestamp

7/18/2013, 7:02:01 AM

Confirmations

6,729,592

Merkle Root

a7a174c9ab02fd6362ffae8f166b5786f172b7083a325a8550c872bd4a8cf353

Transactions (1)

Coinbasea7a174c9ab02fd…c872bd4a8cf353

1 in → 1 out12.4200 XPM110 B

Aa4ciwLf…9b1awN3v

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.

8.529 × 10¹⁰⁴(105-digit number)

85293773687318283385…88330964118950560070

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

8.529 × 10¹⁰⁴(105-digit number)

85293773687318283385…88330964118950560069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.529 × 10¹⁰⁴(105-digit number)

85293773687318283385…88330964118950560071

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

1.705 × 10¹⁰⁵(106-digit number)

17058754737463656677…76661928237901120139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.705 × 10¹⁰⁵(106-digit number)

17058754737463656677…76661928237901120141

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

3.411 × 10¹⁰⁵(106-digit number)

34117509474927313354…53323856475802240279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.411 × 10¹⁰⁵(106-digit number)

34117509474927313354…53323856475802240281

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

6.823 × 10¹⁰⁵(106-digit number)

68235018949854626708…06647712951604480559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.823 × 10¹⁰⁵(106-digit number)

68235018949854626708…06647712951604480561

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

1.364 × 10¹⁰⁶(107-digit number)

13647003789970925341…13295425903208961119

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 60269

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 e6fd238e01f47e09f86943c13a50f8ecfbc2ea35ca8bd31581f100cd4cf063b6

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 #60,269 on Chainz ↗