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Block #301,557

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2013, 6:50:54 AM Β· Difficulty 9.9925 Β· 6,495,040 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d04fdfd69c9aa55b76d61d7915044f41d88b8a26e603e5e3bbc9945a7757b971
View on Chainz β†—

Height

#301,557

Difficulty

9.992530

Transactions

1

Size

206 B

Version

2

Bits

09fe167a

Nonce

305,006

Timestamp

12/9/2013, 6:50:54 AM

Confirmations

6,495,040

Merkle Root

deaaa73363dd9ac0a56c951d70a1c3a1231338b144a35199ea93e31d6c813d4c
Transactions (1)
Coinbasedeaaa73363dd9a…93e31d6c813d4c
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

1.024 Γ— 10⁹⁡(96-digit number)
10244073432262241932…78466519187276446720
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
1.024 Γ— 10⁹⁡(96-digit number)
10244073432262241932…78466519187276446719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.024 Γ— 10⁹⁡(96-digit number)
10244073432262241932…78466519187276446721
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
2.048 Γ— 10⁹⁡(96-digit number)
20488146864524483864…56933038374552893439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.048 Γ— 10⁹⁡(96-digit number)
20488146864524483864…56933038374552893441
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
4.097 Γ— 10⁹⁡(96-digit number)
40976293729048967728…13866076749105786879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.097 Γ— 10⁹⁡(96-digit number)
40976293729048967728…13866076749105786881
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
8.195 Γ— 10⁹⁡(96-digit number)
81952587458097935457…27732153498211573759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.195 Γ— 10⁹⁡(96-digit number)
81952587458097935457…27732153498211573761
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
1.639 Γ— 10⁹⁢(97-digit number)
16390517491619587091…55464306996423147519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.639 Γ— 10⁹⁢(97-digit number)
16390517491619587091…55464306996423147521
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 301557

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 d04fdfd69c9aa55b76d61d7915044f41d88b8a26e603e5e3bbc9945a7757b971

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 #301,557 on Chainz β†—
Circulating Supply:57,616,779 XPMΒ·at block #6,796,596 Β· updates every 60s
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