XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,870,631

Block #2,870,631

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/7/2018, 4:02:30 AM Β· Difficulty 11.6651 Β· 3,968,212 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e407ff3a307b3442f0fdf078637579e8239a48288149a428e4045d5929976464
View on Chainz β†—

Difficulty

11.665112

Transactions

1

Size

200 B

Version

2

Bits

0baa44c0

Nonce

1,561,287,898

Timestamp

10/7/2018, 4:02:30 AM

Confirmations

3,968,212

Merkle Root

2ff300cec4b48701fd4683fca2748b26bb159d5e41beba962be42507d59334d1
Transactions (1)
Coinbase2ff300cec4b487…e42507d59334d1
1 in β†’ 1 out7.3400 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.419 Γ— 10⁹⁴(95-digit number)
34195479571398899637…03582483577281740800
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
3.419 Γ— 10⁹⁴(95-digit number)
34195479571398899637…03582483577281740799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.419 Γ— 10⁹⁴(95-digit number)
34195479571398899637…03582483577281740801
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
6.839 Γ— 10⁹⁴(95-digit number)
68390959142797799274…07164967154563481599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.839 Γ— 10⁹⁴(95-digit number)
68390959142797799274…07164967154563481601
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
1.367 Γ— 10⁹⁡(96-digit number)
13678191828559559854…14329934309126963199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.367 Γ— 10⁹⁡(96-digit number)
13678191828559559854…14329934309126963201
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
2.735 Γ— 10⁹⁡(96-digit number)
27356383657119119709…28659868618253926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.735 Γ— 10⁹⁡(96-digit number)
27356383657119119709…28659868618253926401
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
5.471 Γ— 10⁹⁡(96-digit number)
54712767314238239419…57319737236507852799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.471 Γ— 10⁹⁡(96-digit number)
54712767314238239419…57319737236507852801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.094 Γ— 10⁹⁢(97-digit number)
10942553462847647883…14639474473015705599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2870631

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 e407ff3a307b3442f0fdf078637579e8239a48288149a428e4045d5929976464

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 #2,870,631 on Chainz β†—
Circulating Supply:57,955,006 XPMΒ·at block #6,838,842 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