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Block #304,202

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/10/2013, 7:16:01 PM Β· Difficulty 9.9933 Β· 6,508,462 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
df5432955c7cd5a2840a0171ed9e2a5d1668f7f307154b3f2d25a468eff3aa67
View on Chainz β†—

Height

#304,202

Difficulty

9.993261

Transactions

1

Size

196 B

Version

2

Bits

09fe465a

Nonce

4,618

Timestamp

12/10/2013, 7:16:01 PM

Confirmations

6,508,462

Merkle Root

7bc7def7f872845d70a436cc635e32a03ba60171f4bfcaab32cbc15eb4f3a31f
Transactions (1)
Coinbase7bc7def7f87284…cbc15eb4f3a31f
1 in β†’ 1 out10.0000 XPM109 B
AazFfLyh…JCjRnnHq
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.

1.628 Γ— 10⁸⁸(89-digit number)
16288107443494096140…14143742324745674780
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
1.628 Γ— 10⁸⁸(89-digit number)
16288107443494096140…14143742324745674779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.628 Γ— 10⁸⁸(89-digit number)
16288107443494096140…14143742324745674781
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
3.257 Γ— 10⁸⁸(89-digit number)
32576214886988192281…28287484649491349559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.257 Γ— 10⁸⁸(89-digit number)
32576214886988192281…28287484649491349561
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
6.515 Γ— 10⁸⁸(89-digit number)
65152429773976384563…56574969298982699119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.515 Γ— 10⁸⁸(89-digit number)
65152429773976384563…56574969298982699121
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
1.303 Γ— 10⁸⁹(90-digit number)
13030485954795276912…13149938597965398239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.303 Γ— 10⁸⁹(90-digit number)
13030485954795276912…13149938597965398241
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
2.606 Γ— 10⁸⁹(90-digit number)
26060971909590553825…26299877195930796479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.606 Γ— 10⁸⁹(90-digit number)
26060971909590553825…26299877195930796481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 304202

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 df5432955c7cd5a2840a0171ed9e2a5d1668f7f307154b3f2d25a468eff3aa67

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 #304,202 on Chainz β†—
Circulating Supply:57,745,343 XPMΒ·at block #6,812,663 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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