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Block #850,090

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/12/2014, 6:43:38 AM Β· Difficulty 10.9713 Β· 5,994,655 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cccee1c0b94a8944e014b23f6fd1e45df6824511dc4ec1b6101235878c537e48
View on Chainz β†—

Height

#850,090

Difficulty

10.971332

Transactions

1

Size

200 B

Version

2

Bits

0af8a934

Nonce

1,110,625,731

Timestamp

12/12/2014, 6:43:38 AM

Confirmations

5,994,655

Merkle Root

0b814a87be978e93b02de3313d698d3d8c3b5a21deab1b637ef02fff69596552
Transactions (1)
Coinbase0b814a87be978e…f02fff69596552
1 in β†’ 1 out8.2900 XPM109 B
Af7Ds9iQ…hrt5qAvo
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.

1.415 Γ— 10⁹⁷(98-digit number)
14150754096488712676…47309604679396602880
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
1.415 Γ— 10⁹⁷(98-digit number)
14150754096488712676…47309604679396602879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.415 Γ— 10⁹⁷(98-digit number)
14150754096488712676…47309604679396602881
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
2.830 Γ— 10⁹⁷(98-digit number)
28301508192977425353…94619209358793205759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.830 Γ— 10⁹⁷(98-digit number)
28301508192977425353…94619209358793205761
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
5.660 Γ— 10⁹⁷(98-digit number)
56603016385954850706…89238418717586411519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.660 Γ— 10⁹⁷(98-digit number)
56603016385954850706…89238418717586411521
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
1.132 Γ— 10⁹⁸(99-digit number)
11320603277190970141…78476837435172823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.132 Γ— 10⁹⁸(99-digit number)
11320603277190970141…78476837435172823041
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
2.264 Γ— 10⁹⁸(99-digit number)
22641206554381940282…56953674870345646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.264 Γ— 10⁹⁸(99-digit number)
22641206554381940282…56953674870345646081
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 850090

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 cccee1c0b94a8944e014b23f6fd1e45df6824511dc4ec1b6101235878c537e48

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 #850,090 on Chainz β†—
Circulating Supply:58,002,373 XPMΒ·at block #6,844,744 Β· updates every 60s
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