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Block #601,162

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2014, 7:51:51 AM · Difficulty 10.9154 · 6,211,570 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3891c8f02397cbc278934f35d4d108ddcdf2e457bad96f0e70d177545621e43d

View on Chainz ↗

Height

#601,162

Difficulty

10.915394

Transactions

Size

436 B

Version

Bits

0aea5746

Nonce

399,853,585

Timestamp

6/25/2014, 7:51:51 AM

Confirmations

6,211,570

Merkle Root

207858d753c3644364c007e5d14951c3a5a8f761b11d7a1ab64babe2c30b3756

Transactions (2)

Coinbasea887b8697cfb82…21adfd44b6f896

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

459f16d4ce3e3c…72216fc13bb833

1 in → 2 out6.0851 XPM227 B

AQbXQJ4K…SZFydyis AXahbhoN…C7LCDGba

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.

2.570 × 10¹⁰¹(102-digit number)

25705011985906109688…86685293793541160960

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

2.570 × 10¹⁰¹(102-digit number)

25705011985906109688…86685293793541160959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.570 × 10¹⁰¹(102-digit number)

25705011985906109688…86685293793541160961

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

5.141 × 10¹⁰¹(102-digit number)

51410023971812219376…73370587587082321919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.141 × 10¹⁰¹(102-digit number)

51410023971812219376…73370587587082321921

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

1.028 × 10¹⁰²(103-digit number)

10282004794362443875…46741175174164643839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.028 × 10¹⁰²(103-digit number)

10282004794362443875…46741175174164643841

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

2.056 × 10¹⁰²(103-digit number)

20564009588724887750…93482350348329287679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.056 × 10¹⁰²(103-digit number)

20564009588724887750…93482350348329287681

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

4.112 × 10¹⁰²(103-digit number)

41128019177449775501…86964700696658575359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.112 × 10¹⁰²(103-digit number)

41128019177449775501…86964700696658575361

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 601162

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 3891c8f02397cbc278934f35d4d108ddcdf2e457bad96f0e70d177545621e43d

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 #601,162 on Chainz ↗

Block #601,162

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