XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,860,371

Block #2,860,371

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2018, 10:27:57 PM Β· Difficulty 11.6749 Β· 3,982,450 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
10db74b3d9b014e6d38349888b3275fe07f1066a59ad10a42400fc35ca738b93
View on Chainz β†—

Difficulty

11.674867

Transactions

1

Size

200 B

Version

2

Bits

0bacc418

Nonce

1,376,156,996

Timestamp

9/29/2018, 10:27:57 PM

Confirmations

3,982,450

Merkle Root

022379646e1851a79a0150f0ba0ad62c9990adfed1b045468e94af9da4b3e063
Transactions (1)
Coinbase022379646e1851…94af9da4b3e063
1 in β†’ 1 out7.3200 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.

1.239 Γ— 10⁹⁡(96-digit number)
12398777266164013938…87180812185102347040
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
1.239 Γ— 10⁹⁡(96-digit number)
12398777266164013938…87180812185102347039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.239 Γ— 10⁹⁡(96-digit number)
12398777266164013938…87180812185102347041
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
2.479 Γ— 10⁹⁡(96-digit number)
24797554532328027877…74361624370204694079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.479 Γ— 10⁹⁡(96-digit number)
24797554532328027877…74361624370204694081
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
4.959 Γ— 10⁹⁡(96-digit number)
49595109064656055754…48723248740409388159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.959 Γ— 10⁹⁡(96-digit number)
49595109064656055754…48723248740409388161
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
9.919 Γ— 10⁹⁡(96-digit number)
99190218129312111508…97446497480818776319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.919 Γ— 10⁹⁡(96-digit number)
99190218129312111508…97446497480818776321
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
1.983 Γ— 10⁹⁢(97-digit number)
19838043625862422301…94892994961637552639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.983 Γ— 10⁹⁢(97-digit number)
19838043625862422301…94892994961637552641
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
3.967 Γ— 10⁹⁢(97-digit number)
39676087251724844603…89785989923275105279
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 2860371

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 10db74b3d9b014e6d38349888b3275fe07f1066a59ad10a42400fc35ca738b93

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 #2,860,371 on Chainz β†—
Circulating Supply:57,986,909 XPMΒ·at block #6,842,820 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