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Block #910,092

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 1/26/2015, 1:12:48 AM Β· Difficulty 10.9335 Β· 5,916,486 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cf3f394ea801d868217896aa2a3dc9a3b9df5e8a2cbf65a8c1c886edda95a117
View on Chainz β†—

Height

#910,092

Difficulty

10.933517

Transactions

1

Size

199 B

Version

2

Bits

0aeefafe

Nonce

44,261,079

Timestamp

1/26/2015, 1:12:48 AM

Confirmations

5,916,486

Merkle Root

9289df0d983a2e029fce68d13897ff07f7a7ebbe5f7f6a767d03cfd9e97ad13a
Transactions (1)
Coinbase9289df0d983a2e…03cfd9e97ad13a
1 in β†’ 1 out8.3500 XPM109 B
Aa64RiL8…cBGswrto
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.

4.557 Γ— 10⁹⁴(95-digit number)
45578865315264241507…41215357723887534080
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
4.557 Γ— 10⁹⁴(95-digit number)
45578865315264241507…41215357723887534079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.557 Γ— 10⁹⁴(95-digit number)
45578865315264241507…41215357723887534081
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
9.115 Γ— 10⁹⁴(95-digit number)
91157730630528483015…82430715447775068159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.115 Γ— 10⁹⁴(95-digit number)
91157730630528483015…82430715447775068161
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
1.823 Γ— 10⁹⁡(96-digit number)
18231546126105696603…64861430895550136319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.823 Γ— 10⁹⁡(96-digit number)
18231546126105696603…64861430895550136321
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
3.646 Γ— 10⁹⁡(96-digit number)
36463092252211393206…29722861791100272639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.646 Γ— 10⁹⁡(96-digit number)
36463092252211393206…29722861791100272641
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
7.292 Γ— 10⁹⁡(96-digit number)
72926184504422786412…59445723582200545279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.292 Γ— 10⁹⁡(96-digit number)
72926184504422786412…59445723582200545281
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
1.458 Γ— 10⁹⁢(97-digit number)
14585236900884557282…18891447164401090559
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.458 Γ— 10⁹⁢(97-digit number)
14585236900884557282…18891447164401090561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 910092

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 cf3f394ea801d868217896aa2a3dc9a3b9df5e8a2cbf65a8c1c886edda95a117

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 #910,092 on Chainz β†—
Circulating Supply:57,856,773 XPMΒ·at block #6,826,577 Β· updates every 60s
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