XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #858,571

Block #858,571

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2014, 5:48:57 PM Β· Difficulty 10.9665 Β· 5,965,961 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ff73d1d5831deedc4483499f747c472e72f97798127cd24dc21dd56a9daa9a2e
View on Chainz β†—

Height

#858,571

Difficulty

10.966528

Transactions

1

Size

207 B

Version

2

Bits

0af76e5d

Nonce

1,363,952,746

Timestamp

12/18/2014, 5:48:57 PM

Confirmations

5,965,961

Merkle Root

b698d2fa53d88d20c4ddbac7fd1120d67fb39a87ba4ed02c056d0bf29ba856cc
Transactions (1)
Coinbaseb698d2fa53d88d…6d0bf29ba856cc
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.

2.010 Γ— 10⁹⁢(97-digit number)
20100969073945220382…74729038882558428320
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
2.010 Γ— 10⁹⁢(97-digit number)
20100969073945220382…74729038882558428319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.010 Γ— 10⁹⁢(97-digit number)
20100969073945220382…74729038882558428321
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
4.020 Γ— 10⁹⁢(97-digit number)
40201938147890440764…49458077765116856639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.020 Γ— 10⁹⁢(97-digit number)
40201938147890440764…49458077765116856641
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
8.040 Γ— 10⁹⁢(97-digit number)
80403876295780881528…98916155530233713279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.040 Γ— 10⁹⁢(97-digit number)
80403876295780881528…98916155530233713281
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
1.608 Γ— 10⁹⁷(98-digit number)
16080775259156176305…97832311060467426559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.608 Γ— 10⁹⁷(98-digit number)
16080775259156176305…97832311060467426561
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
3.216 Γ— 10⁹⁷(98-digit number)
32161550518312352611…95664622120934853119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.216 Γ— 10⁹⁷(98-digit number)
32161550518312352611…95664622120934853121
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 858571

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 ff73d1d5831deedc4483499f747c472e72f97798127cd24dc21dd56a9daa9a2e

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 #858,571 on Chainz β†—
Circulating Supply:57,840,321 XPMΒ·at block #6,824,531 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