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Home/Chain Registry/Block #2,303,913

Block #2,303,913

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/21/2017, 8:06:59 PM Β· Difficulty 10.9190 Β· 4,539,208 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27b28907ad8791609de86d30535cd07d3e6c8cc4868a12ceae3391f2933df576
View on Chainz β†—

Difficulty

10.918979

Transactions

1

Size

198 B

Version

2

Bits

0aeb4239

Nonce

1,815,349,268

Timestamp

9/21/2017, 8:06:59 PM

Confirmations

4,539,208

Merkle Root

140c2c443bc512feb044d7f57508e9aa0e6fa70d3a39a623823caeb03aa8db36
Transactions (1)
Coinbase140c2c443bc512…3caeb03aa8db36
1 in β†’ 1 out8.3700 XPM109 B
AL6BMTpr…eZUjFRXz
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.

2.623 Γ— 10⁹²(93-digit number)
26231856778987749977…80584075712377774080
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
2.623 Γ— 10⁹²(93-digit number)
26231856778987749977…80584075712377774079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.623 Γ— 10⁹²(93-digit number)
26231856778987749977…80584075712377774081
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
5.246 Γ— 10⁹²(93-digit number)
52463713557975499954…61168151424755548159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.246 Γ— 10⁹²(93-digit number)
52463713557975499954…61168151424755548161
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
1.049 Γ— 10⁹³(94-digit number)
10492742711595099990…22336302849511096319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.049 Γ— 10⁹³(94-digit number)
10492742711595099990…22336302849511096321
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
2.098 Γ— 10⁹³(94-digit number)
20985485423190199981…44672605699022192639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.098 Γ— 10⁹³(94-digit number)
20985485423190199981…44672605699022192641
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
4.197 Γ— 10⁹³(94-digit number)
41970970846380399963…89345211398044385279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.197 Γ— 10⁹³(94-digit number)
41970970846380399963…89345211398044385281
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 2303913

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 27b28907ad8791609de86d30535cd07d3e6c8cc4868a12ceae3391f2933df576

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 #2,303,913 on Chainz β†—
Circulating Supply:57,989,333 XPMΒ·at block #6,843,120 Β· updates every 60s
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