XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #207,448

Block #207,448

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2013, 11:05:55 AM Β· Difficulty 9.9026 Β· 6,596,525 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe14d0b44e68cc163b6bded6094bb3f4ced39473c265429799ac1dd50312c9cb
View on Chainz β†—

Height

#207,448

Difficulty

9.902624

Transactions

1

Size

198 B

Version

2

Bits

09e7125f

Nonce

84,354

Timestamp

10/13/2013, 11:05:55 AM

Confirmations

6,596,525

Merkle Root

5e53a44a83b0feed7b9ab526d998c4f6ac28c9d428fc18ef090f219baa1a8293
Transactions (1)
Coinbase5e53a44a83b0fe…0f219baa1a8293
1 in β†’ 1 out10.1800 XPM109 B
AdYjS2Ea…LEnjyFLD
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.

6.968 Γ— 10⁹¹(92-digit number)
69688497135292708332…40065716542178326400
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
6.968 Γ— 10⁹¹(92-digit number)
69688497135292708332…40065716542178326399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.968 Γ— 10⁹¹(92-digit number)
69688497135292708332…40065716542178326401
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
1.393 Γ— 10⁹²(93-digit number)
13937699427058541666…80131433084356652799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.393 Γ— 10⁹²(93-digit number)
13937699427058541666…80131433084356652801
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
2.787 Γ— 10⁹²(93-digit number)
27875398854117083332…60262866168713305599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.787 Γ— 10⁹²(93-digit number)
27875398854117083332…60262866168713305601
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
5.575 Γ— 10⁹²(93-digit number)
55750797708234166665…20525732337426611199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.575 Γ— 10⁹²(93-digit number)
55750797708234166665…20525732337426611201
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
1.115 Γ— 10⁹³(94-digit number)
11150159541646833333…41051464674853222399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.115 Γ— 10⁹³(94-digit number)
11150159541646833333…41051464674853222401
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
2.230 Γ— 10⁹³(94-digit number)
22300319083293666666…82102929349706444799
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 207448

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 fe14d0b44e68cc163b6bded6094bb3f4ced39473c265429799ac1dd50312c9cb

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 #207,448 on Chainz β†—
Circulating Supply:57,675,831 XPMΒ·at block #6,803,972 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK