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Home/Chain Registry/Block #2,598,227

Block #2,598,227

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2018, 9:45:43 AM Β· Difficulty 11.3155 Β· 4,226,792 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6177a36ffc362926473a63d3dfc31d1985ce0f2c9aed8b0ed22deec2a70b6520
View on Chainz β†—

Difficulty

11.315492

Transactions

1

Size

200 B

Version

2

Bits

0b50c41a

Nonce

1,109,249,377

Timestamp

4/3/2018, 9:45:43 AM

Confirmations

4,226,792

Merkle Root

4542a69f80f7c2e35cc77a255e723eee65ece92d9bef9fe593ee6062209776c0
Transactions (1)
Coinbase4542a69f80f7c2…ee6062209776c0
1 in β†’ 1 out7.8000 XPM110 B
AY3DsDPv…Bk3GSHm9
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.

4.059 Γ— 10⁹⁡(96-digit number)
40594306442427888838…86619131535967185920
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
4.059 Γ— 10⁹⁡(96-digit number)
40594306442427888838…86619131535967185919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.059 Γ— 10⁹⁡(96-digit number)
40594306442427888838…86619131535967185921
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
8.118 Γ— 10⁹⁡(96-digit number)
81188612884855777677…73238263071934371839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.118 Γ— 10⁹⁡(96-digit number)
81188612884855777677…73238263071934371841
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
1.623 Γ— 10⁹⁢(97-digit number)
16237722576971155535…46476526143868743679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.623 Γ— 10⁹⁢(97-digit number)
16237722576971155535…46476526143868743681
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
3.247 Γ— 10⁹⁢(97-digit number)
32475445153942311070…92953052287737487359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.247 Γ— 10⁹⁢(97-digit number)
32475445153942311070…92953052287737487361
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
6.495 Γ— 10⁹⁢(97-digit number)
64950890307884622141…85906104575474974719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.495 Γ— 10⁹⁢(97-digit number)
64950890307884622141…85906104575474974721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁷(98-digit number)
12990178061576924428…71812209150949949439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2598227

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 6177a36ffc362926473a63d3dfc31d1985ce0f2c9aed8b0ed22deec2a70b6520

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 #2,598,227 on Chainz β†—
Circulating Supply:57,844,235 XPMΒ·at block #6,825,018 Β· updates every 60s
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