XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #203,302

Block #203,302

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/10/2013, 6:31:24 PM Β· Difficulty 9.8970 Β· 6,623,015 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e78e0eb7d7585776f889875e2cfa6325e3537b4c07f3cc1722b2c63c23e0152d
View on Chainz β†—

Height

#203,302

Difficulty

9.897007

Transactions

1

Size

199 B

Version

2

Bits

09e5a23b

Nonce

56,442

Timestamp

10/10/2013, 6:31:24 PM

Confirmations

6,623,015

Merkle Root

07c303c11cbcb45740b175eccc125f79431e0752edd83eef952c329b15d8ab30
Transactions (1)
Coinbase07c303c11cbcb4…2c329b15d8ab30
1 in β†’ 1 out10.1900 XPM109 B
AG2TjRM9…S7Hdapuf
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.

6.553 Γ— 10⁹³(94-digit number)
65532222897516941374…48178208456743004160
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
6.553 Γ— 10⁹³(94-digit number)
65532222897516941374…48178208456743004159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.553 Γ— 10⁹³(94-digit number)
65532222897516941374…48178208456743004161
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
1.310 Γ— 10⁹⁴(95-digit number)
13106444579503388274…96356416913486008319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.310 Γ— 10⁹⁴(95-digit number)
13106444579503388274…96356416913486008321
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
2.621 Γ— 10⁹⁴(95-digit number)
26212889159006776549…92712833826972016639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.621 Γ— 10⁹⁴(95-digit number)
26212889159006776549…92712833826972016641
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
5.242 Γ— 10⁹⁴(95-digit number)
52425778318013553099…85425667653944033279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.242 Γ— 10⁹⁴(95-digit number)
52425778318013553099…85425667653944033281
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
1.048 Γ— 10⁹⁡(96-digit number)
10485155663602710619…70851335307888066559
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 203302

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 e78e0eb7d7585776f889875e2cfa6325e3537b4c07f3cc1722b2c63c23e0152d

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 #203,302 on Chainz β†—
Circulating Supply:57,854,675 XPMΒ·at block #6,826,316 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