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Home/Chain Registry/Block #1,265,204

Block #1,265,204

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/3/2015, 10:02:50 AM Β· Difficulty 10.8227 Β· 5,561,349 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c6ce2dbce1aa91275d325137f43cd5e17de7a8b2248c826842212506520c870f
View on Chainz β†—

Difficulty

10.822705

Transactions

1

Size

199 B

Version

2

Bits

0ad29cca

Nonce

433,753,551

Timestamp

10/3/2015, 10:02:50 AM

Confirmations

5,561,349

Merkle Root

b911bb6a57ffcee6010072be47dccf0d57dbdf7b8f0dac55960d09379c761496
Transactions (1)
Coinbaseb911bb6a57ffce…0d09379c761496
1 in β†’ 1 out8.5200 XPM109 B
AU2P8Fzw…qxxu3NMm
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.

4.916 Γ— 10⁹⁡(96-digit number)
49168615710105381111…71365051728384922240
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
4.916 Γ— 10⁹⁡(96-digit number)
49168615710105381111…71365051728384922239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.916 Γ— 10⁹⁡(96-digit number)
49168615710105381111…71365051728384922241
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
9.833 Γ— 10⁹⁡(96-digit number)
98337231420210762222…42730103456769844479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.833 Γ— 10⁹⁡(96-digit number)
98337231420210762222…42730103456769844481
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
1.966 Γ— 10⁹⁢(97-digit number)
19667446284042152444…85460206913539688959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.966 Γ— 10⁹⁢(97-digit number)
19667446284042152444…85460206913539688961
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
3.933 Γ— 10⁹⁢(97-digit number)
39334892568084304888…70920413827079377919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.933 Γ— 10⁹⁢(97-digit number)
39334892568084304888…70920413827079377921
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
7.866 Γ— 10⁹⁢(97-digit number)
78669785136168609777…41840827654158755839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.866 Γ— 10⁹⁢(97-digit number)
78669785136168609777…41840827654158755841
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 1265204

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 c6ce2dbce1aa91275d325137f43cd5e17de7a8b2248c826842212506520c870f

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 #1,265,204 on Chainz β†—
Circulating Supply:57,856,574 XPMΒ·at block #6,826,552 Β· updates every 60s
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