XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,872,007

Block #2,872,007

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/8/2018, 2:33:26 AM Β· Difficulty 11.6668 Β· 3,970,780 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
34968d2526f51b01b3aa1002cc8ab070aa31a29cf174e26bc7cee8b6feffeb3f
View on Chainz β†—

Difficulty

11.666809

Transactions

1

Size

200 B

Version

2

Bits

0baab402

Nonce

149,572,514

Timestamp

10/8/2018, 2:33:26 AM

Confirmations

3,970,780

Merkle Root

3c902fbd608f7cb7eb37fd33eeb1d1f98bcdadfb810b220154d527a484610b37
Transactions (1)
Coinbase3c902fbd608f7c…d527a484610b37
1 in β†’ 1 out7.3300 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.

3.354 Γ— 10⁹⁴(95-digit number)
33540373728861441729…55799123429311955100
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
3.354 Γ— 10⁹⁴(95-digit number)
33540373728861441729…55799123429311955099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.354 Γ— 10⁹⁴(95-digit number)
33540373728861441729…55799123429311955101
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
6.708 Γ— 10⁹⁴(95-digit number)
67080747457722883459…11598246858623910199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.708 Γ— 10⁹⁴(95-digit number)
67080747457722883459…11598246858623910201
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
1.341 Γ— 10⁹⁡(96-digit number)
13416149491544576691…23196493717247820399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.341 Γ— 10⁹⁡(96-digit number)
13416149491544576691…23196493717247820401
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
2.683 Γ— 10⁹⁡(96-digit number)
26832298983089153383…46392987434495640799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.683 Γ— 10⁹⁡(96-digit number)
26832298983089153383…46392987434495640801
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
5.366 Γ— 10⁹⁡(96-digit number)
53664597966178306767…92785974868991281599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.366 Γ— 10⁹⁡(96-digit number)
53664597966178306767…92785974868991281601
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
1.073 Γ— 10⁹⁢(97-digit number)
10732919593235661353…85571949737982563199
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 2872007

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 34968d2526f51b01b3aa1002cc8ab070aa31a29cf174e26bc7cee8b6feffeb3f

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 #2,872,007 on Chainz β†—
Circulating Supply:57,986,636 XPMΒ·at block #6,842,786 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