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Home/Chain Registry/Block #1,055,866

Block #1,055,866

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/12/2015, 8:57:37 AM Β· Difficulty 10.7259 Β· 5,787,205 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5e772933e2854b4b18fd8a3daedd73e34231de2d508e4666101acf9d73b00f8
View on Chainz β†—

Difficulty

10.725941

Transactions

1

Size

207 B

Version

2

Bits

0ab9d74a

Nonce

256,463,962

Timestamp

5/12/2015, 8:57:37 AM

Confirmations

5,787,205

Merkle Root

393e8f9ab3f8d1f80c0b1e7ff22863bd0b063f2e91c4de32a0ba40aafb9d7a78
Transactions (1)
Coinbase393e8f9ab3f8d1…ba40aafb9d7a78
1 in β†’ 1 out8.6800 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.

1.223 Γ— 10⁹⁸(99-digit number)
12230813396221426008…24180659248746168320
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
1.223 Γ— 10⁹⁸(99-digit number)
12230813396221426008…24180659248746168319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.223 Γ— 10⁹⁸(99-digit number)
12230813396221426008…24180659248746168321
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
2.446 Γ— 10⁹⁸(99-digit number)
24461626792442852017…48361318497492336639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.446 Γ— 10⁹⁸(99-digit number)
24461626792442852017…48361318497492336641
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
4.892 Γ— 10⁹⁸(99-digit number)
48923253584885704034…96722636994984673279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.892 Γ— 10⁹⁸(99-digit number)
48923253584885704034…96722636994984673281
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
9.784 Γ— 10⁹⁸(99-digit number)
97846507169771408069…93445273989969346559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.784 Γ— 10⁹⁸(99-digit number)
97846507169771408069…93445273989969346561
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
1.956 Γ— 10⁹⁹(100-digit number)
19569301433954281613…86890547979938693119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.956 Γ— 10⁹⁹(100-digit number)
19569301433954281613…86890547979938693121
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
3.913 Γ— 10⁹⁹(100-digit number)
39138602867908563227…73781095959877386239
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 1055866

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 a5e772933e2854b4b18fd8a3daedd73e34231de2d508e4666101acf9d73b00f8

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 #1,055,866 on Chainz β†—
Circulating Supply:57,988,927 XPMΒ·at block #6,843,070 Β· updates every 60s
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