XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #570,248

Block #570,248

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/31/2014, 4:42:37 PM Β· Difficulty 10.9649 Β· 6,255,281 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1dbd3e98d5812c5ba2ccfd09b9d0cd89ffe10d7f3769eedc9fd860ad01e46243
View on Chainz β†—

Height

#570,248

Difficulty

10.964918

Transactions

1

Size

209 B

Version

2

Bits

0af704e4

Nonce

322,161,727

Timestamp

5/31/2014, 4:42:37 PM

Confirmations

6,255,281

Merkle Root

79b61e558174ea7572424c1f8f9da47bdfa2edbe4a66f6f4b0fe9f618ab1ca80
Transactions (1)
Coinbase79b61e558174ea…fe9f618ab1ca80
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.015 Γ— 10¹⁰⁰(101-digit number)
50155717732581004611…16497188813676912640
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.015 Γ— 10¹⁰⁰(101-digit number)
50155717732581004611…16497188813676912639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.015 Γ— 10¹⁰⁰(101-digit number)
50155717732581004611…16497188813676912641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.003 Γ— 10¹⁰¹(102-digit number)
10031143546516200922…32994377627353825279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.003 Γ— 10¹⁰¹(102-digit number)
10031143546516200922…32994377627353825281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.006 Γ— 10¹⁰¹(102-digit number)
20062287093032401844…65988755254707650559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.006 Γ— 10¹⁰¹(102-digit number)
20062287093032401844…65988755254707650561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.012 Γ— 10¹⁰¹(102-digit number)
40124574186064803689…31977510509415301119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.012 Γ— 10¹⁰¹(102-digit number)
40124574186064803689…31977510509415301121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
8.024 Γ— 10¹⁰¹(102-digit number)
80249148372129607378…63955021018830602239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.024 Γ— 10¹⁰¹(102-digit number)
80249148372129607378…63955021018830602241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 570248

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 1dbd3e98d5812c5ba2ccfd09b9d0cd89ffe10d7f3769eedc9fd860ad01e46243

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 β†’ Debug Window β†’ 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 #570,248 on Chainz β†—
Circulating Supply:57,848,329 XPMΒ·at block #6,825,528 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy