XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #102,425

Block #102,425

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2013, 3:11:37 AM Β· Difficulty 9.4930 Β· 6,696,147 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c12d8188e725f44a8de7a3d9e689e39ae6dfafb61842060669f02103a65f26e
View on Chainz β†—

Height

#102,425

Difficulty

9.493024

Transactions

2

Size

3.02 KB

Version

2

Bits

097e36d7

Nonce

664,060

Timestamp

8/7/2013, 3:11:37 AM

Confirmations

6,696,147

Merkle Root

d712ed53316ff2559b2e4c7adc6211dbc1fb242df744f14410150c2b57fce844
Transactions (2)
Coinbase9fc4601620c5ba…666a78b08f151a
1 in β†’ 1 out11.1100 XPM109 B
AaW6NMBQ…pGgY9nnc
3d8af6721eb506…a5751ab7d9e546
25 in β†’ 1 out311.0000 XPM2.82 KB
AWqrmbWo…ZcSjTJTw
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.

1.013 Γ— 10⁹⁡(96-digit number)
10136015285425956083…82595216378442405330
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
1.013 Γ— 10⁹⁡(96-digit number)
10136015285425956083…82595216378442405329
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.013 Γ— 10⁹⁡(96-digit number)
10136015285425956083…82595216378442405331
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
2.027 Γ— 10⁹⁡(96-digit number)
20272030570851912166…65190432756884810659
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.027 Γ— 10⁹⁡(96-digit number)
20272030570851912166…65190432756884810661
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
4.054 Γ— 10⁹⁡(96-digit number)
40544061141703824332…30380865513769621319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.054 Γ— 10⁹⁡(96-digit number)
40544061141703824332…30380865513769621321
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
8.108 Γ— 10⁹⁡(96-digit number)
81088122283407648665…60761731027539242639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.108 Γ— 10⁹⁡(96-digit number)
81088122283407648665…60761731027539242641
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
1.621 Γ— 10⁹⁢(97-digit number)
16217624456681529733…21523462055078485279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 102425

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 0c12d8188e725f44a8de7a3d9e689e39ae6dfafb61842060669f02103a65f26e

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 #102,425 on Chainz β†—
Circulating Supply:57,632,594 XPMΒ·at block #6,798,571 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