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Home/Chain Registry/Block #2,528,598

Block #2,528,598

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/19/2018, 12:24:30 PM Β· Difficulty 10.9847 Β· 4,315,106 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
281a89868cf2fcbf0ebd51bb51afd020915013272f98d93e941c94ee2c9a5c14
View on Chainz β†—

Difficulty

10.984655

Transactions

1

Size

200 B

Version

2

Bits

0afc1253

Nonce

872,328,167

Timestamp

2/19/2018, 12:24:30 PM

Confirmations

4,315,106

Merkle Root

8bf82f61081cba6f3c4cb9c360ae1a0e4cc270e62252af3d13ab0f8c7932c4de
Transactions (1)
Coinbase8bf82f61081cba…ab0f8c7932c4de
1 in β†’ 1 out8.2700 XPM110 B
Ab758vur…rKcsRFSN
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.

9.115 Γ— 10⁹³(94-digit number)
91156337056357899974…50240462962337273920
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
9.115 Γ— 10⁹³(94-digit number)
91156337056357899974…50240462962337273919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.115 Γ— 10⁹³(94-digit number)
91156337056357899974…50240462962337273921
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
1.823 Γ— 10⁹⁴(95-digit number)
18231267411271579994…00480925924674547839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.823 Γ— 10⁹⁴(95-digit number)
18231267411271579994…00480925924674547841
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
3.646 Γ— 10⁹⁴(95-digit number)
36462534822543159989…00961851849349095679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.646 Γ— 10⁹⁴(95-digit number)
36462534822543159989…00961851849349095681
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
7.292 Γ— 10⁹⁴(95-digit number)
72925069645086319979…01923703698698191359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.292 Γ— 10⁹⁴(95-digit number)
72925069645086319979…01923703698698191361
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
1.458 Γ— 10⁹⁡(96-digit number)
14585013929017263995…03847407397396382719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.458 Γ— 10⁹⁡(96-digit number)
14585013929017263995…03847407397396382721
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
2.917 Γ— 10⁹⁡(96-digit number)
29170027858034527991…07694814794792765439
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 2528598

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 281a89868cf2fcbf0ebd51bb51afd020915013272f98d93e941c94ee2c9a5c14

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 #2,528,598 on Chainz β†—
Circulating Supply:57,994,001 XPMΒ·at block #6,843,703 Β· updates every 60s
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