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Home/Chain Registry/Block #2,634,253

Block #2,634,253

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 7:55:33 PM Β· Difficulty 11.2330 Β· 4,197,696 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec05ac022cf0bd82c894fca46caf1311dd17348516f8e661f3c2b7732503244e
View on Chainz β†—

Difficulty

11.232958

Transactions

1

Size

199 B

Version

2

Bits

0b3ba31e

Nonce

14,468,621

Timestamp

4/28/2018, 7:55:33 PM

Confirmations

4,197,696

Merkle Root

08829c0eead711ade0b95b28eab9b520e016e5c267f4ccd2d58d5f48bda3ad5c
Transactions (1)
Coinbase08829c0eead711…8d5f48bda3ad5c
1 in β†’ 1 out7.9100 XPM110 B
AZVUHuy5…Y2w5CQfm
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.

7.437 Γ— 10⁹²(93-digit number)
74379487132302962511…20185210793072598560
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
7.437 Γ— 10⁹²(93-digit number)
74379487132302962511…20185210793072598559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.437 Γ— 10⁹²(93-digit number)
74379487132302962511…20185210793072598561
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
1.487 Γ— 10⁹³(94-digit number)
14875897426460592502…40370421586145197119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.487 Γ— 10⁹³(94-digit number)
14875897426460592502…40370421586145197121
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
2.975 Γ— 10⁹³(94-digit number)
29751794852921185004…80740843172290394239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.975 Γ— 10⁹³(94-digit number)
29751794852921185004…80740843172290394241
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
5.950 Γ— 10⁹³(94-digit number)
59503589705842370009…61481686344580788479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.950 Γ— 10⁹³(94-digit number)
59503589705842370009…61481686344580788481
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
1.190 Γ— 10⁹⁴(95-digit number)
11900717941168474001…22963372689161576959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.190 Γ— 10⁹⁴(95-digit number)
11900717941168474001…22963372689161576961
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
2.380 Γ— 10⁹⁴(95-digit number)
23801435882336948003…45926745378323153919
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 2634253

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 ec05ac022cf0bd82c894fca46caf1311dd17348516f8e661f3c2b7732503244e

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 #2,634,253 on Chainz β†—
Circulating Supply:57,899,712 XPMΒ·at block #6,831,948 Β· updates every 60s
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