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Home/Chain Registry/Block #1,085,810

Block #1,085,810

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2015, 6:46:22 PM Β· Difficulty 10.7556 Β· 5,722,275 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c7ee8d4ab354401bfbf237444e4e627a3ba41b570cbed69de8d6f476cd6a42bc
View on Chainz β†—

Difficulty

10.755620

Transactions

1

Size

206 B

Version

2

Bits

0ac17055

Nonce

1,527,648,608

Timestamp

6/1/2015, 6:46:22 PM

Confirmations

5,722,275

Merkle Root

1fa29f8ab34d91c4b1d1cd76e2c3a76fbd3e5242eab70bde2937ce4ffa3d21b1
Transactions (1)
Coinbase1fa29f8ab34d91…37ce4ffa3d21b1
1 in β†’ 1 out8.6300 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.709 Γ— 10⁹⁡(96-digit number)
47099331325213214156…92929393869625772500
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
4.709 Γ— 10⁹⁡(96-digit number)
47099331325213214156…92929393869625772499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.709 Γ— 10⁹⁡(96-digit number)
47099331325213214156…92929393869625772501
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
9.419 Γ— 10⁹⁡(96-digit number)
94198662650426428313…85858787739251544999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.419 Γ— 10⁹⁡(96-digit number)
94198662650426428313…85858787739251545001
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
1.883 Γ— 10⁹⁢(97-digit number)
18839732530085285662…71717575478503089999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.883 Γ— 10⁹⁢(97-digit number)
18839732530085285662…71717575478503090001
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
3.767 Γ— 10⁹⁢(97-digit number)
37679465060170571325…43435150957006179999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.767 Γ— 10⁹⁢(97-digit number)
37679465060170571325…43435150957006180001
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
7.535 Γ— 10⁹⁢(97-digit number)
75358930120341142651…86870301914012359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.535 Γ— 10⁹⁢(97-digit number)
75358930120341142651…86870301914012360001
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 1085810

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 c7ee8d4ab354401bfbf237444e4e627a3ba41b570cbed69de8d6f476cd6a42bc

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 #1,085,810 on Chainz β†—
Circulating Supply:57,708,728 XPMΒ·at block #6,808,084 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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