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Block #839,727

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2014, 3:07:32 PM Β· Difficulty 10.9745 Β· 6,005,463 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ced8cf19daad3547d26a894aaa7e06d2cfd03cb1b95f2e74827b4263945058ea
View on Chainz β†—

Height

#839,727

Difficulty

10.974524

Transactions

1

Size

200 B

Version

2

Bits

0af97a6a

Nonce

721,688,547

Timestamp

12/4/2014, 3:07:32 PM

Confirmations

6,005,463

Merkle Root

88d234c158e16918c0fcfee0166aeb371c62527df74e57fefcf455a6cd472a6c
Transactions (1)
Coinbase88d234c158e169…f455a6cd472a6c
1 in β†’ 1 out8.2900 XPM109 B
AckZh7CR…qihZ6mGY
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.

6.717 Γ— 10⁹⁷(98-digit number)
67178749400125119351…53650598125462159360
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
6.717 Γ— 10⁹⁷(98-digit number)
67178749400125119351…53650598125462159359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.717 Γ— 10⁹⁷(98-digit number)
67178749400125119351…53650598125462159361
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
1.343 Γ— 10⁹⁸(99-digit number)
13435749880025023870…07301196250924318719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.343 Γ— 10⁹⁸(99-digit number)
13435749880025023870…07301196250924318721
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
2.687 Γ— 10⁹⁸(99-digit number)
26871499760050047740…14602392501848637439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.687 Γ— 10⁹⁸(99-digit number)
26871499760050047740…14602392501848637441
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
5.374 Γ— 10⁹⁸(99-digit number)
53742999520100095480…29204785003697274879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.374 Γ— 10⁹⁸(99-digit number)
53742999520100095480…29204785003697274881
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
1.074 Γ— 10⁹⁹(100-digit number)
10748599904020019096…58409570007394549759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.074 Γ— 10⁹⁹(100-digit number)
10748599904020019096…58409570007394549761
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
2.149 Γ— 10⁹⁹(100-digit number)
21497199808040038192…16819140014789099519
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 839727

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 ced8cf19daad3547d26a894aaa7e06d2cfd03cb1b95f2e74827b4263945058ea

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 #839,727 on Chainz β†—
Circulating Supply:58,005,950 XPMΒ·at block #6,845,189 Β· updates every 60s
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