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Home/Chain Registry/Block #2,457,166

Block #2,457,166

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2018, 11:26:09 AM Β· Difficulty 10.9539 Β· 4,385,268 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c09259e1db5ecbc4b724f3d7bddec40cf645daf30c9b9dbd54ea8f4da96aaa3d
View on Chainz β†—

Difficulty

10.953906

Transactions

1

Size

199 B

Version

2

Bits

0af4332a

Nonce

686,078,038

Timestamp

1/4/2018, 11:26:09 AM

Confirmations

4,385,268

Merkle Root

a02e1b912b3b64e8d945d49500db1ceb4c6f1404f2c3e43c2c6450971d8ecdb3
Transactions (1)
Coinbasea02e1b912b3b64…6450971d8ecdb3
1 in β†’ 1 out8.3200 XPM110 B
ARmdpjxM…afcZvTDM
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.

5.665 Γ— 10⁹²(93-digit number)
56652298499007376042…79588628245692275040
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
5.665 Γ— 10⁹²(93-digit number)
56652298499007376042…79588628245692275039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.665 Γ— 10⁹²(93-digit number)
56652298499007376042…79588628245692275041
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
1.133 Γ— 10⁹³(94-digit number)
11330459699801475208…59177256491384550079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.133 Γ— 10⁹³(94-digit number)
11330459699801475208…59177256491384550081
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
2.266 Γ— 10⁹³(94-digit number)
22660919399602950417…18354512982769100159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.266 Γ— 10⁹³(94-digit number)
22660919399602950417…18354512982769100161
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
4.532 Γ— 10⁹³(94-digit number)
45321838799205900834…36709025965538200319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.532 Γ— 10⁹³(94-digit number)
45321838799205900834…36709025965538200321
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
9.064 Γ— 10⁹³(94-digit number)
90643677598411801668…73418051931076400639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.064 Γ— 10⁹³(94-digit number)
90643677598411801668…73418051931076400641
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 2457166

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 c09259e1db5ecbc4b724f3d7bddec40cf645daf30c9b9dbd54ea8f4da96aaa3d

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 #2,457,166 on Chainz β†—
Circulating Supply:57,983,888 XPMΒ·at block #6,842,433 Β· updates every 60s
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