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Home/Chain Registry/Block #1,145,562

Block #1,145,562

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/8/2015, 10:06:50 PM Β· Difficulty 10.9309 Β· 5,695,771 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3bffde9082f5bb6d1e7fd2598f9acd09199f89e1e0d284d0e51a9d1df5c04ede
View on Chainz β†—

Difficulty

10.930923

Transactions

1

Size

200 B

Version

2

Bits

0aee50f3

Nonce

1,108,071,043

Timestamp

7/8/2015, 10:06:50 PM

Confirmations

5,695,771

Merkle Root

778e6fad7a7b1afb6e7d92d22a011fec5844be7cb138ddaf6f9a0cfcbb48c6ae
Transactions (1)
Coinbase778e6fad7a7b1a…9a0cfcbb48c6ae
1 in β†’ 1 out8.3600 XPM110 B
AeNNfyKf…cJZgoz4A
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.

1.742 Γ— 10⁹⁡(96-digit number)
17422990940480976408…35065313919217419520
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
1.742 Γ— 10⁹⁡(96-digit number)
17422990940480976408…35065313919217419519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.742 Γ— 10⁹⁡(96-digit number)
17422990940480976408…35065313919217419521
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
3.484 Γ— 10⁹⁡(96-digit number)
34845981880961952816…70130627838434839039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.484 Γ— 10⁹⁡(96-digit number)
34845981880961952816…70130627838434839041
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
6.969 Γ— 10⁹⁡(96-digit number)
69691963761923905632…40261255676869678079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.969 Γ— 10⁹⁡(96-digit number)
69691963761923905632…40261255676869678081
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
1.393 Γ— 10⁹⁢(97-digit number)
13938392752384781126…80522511353739356159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.393 Γ— 10⁹⁢(97-digit number)
13938392752384781126…80522511353739356161
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
2.787 Γ— 10⁹⁢(97-digit number)
27876785504769562252…61045022707478712319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.787 Γ— 10⁹⁢(97-digit number)
27876785504769562252…61045022707478712321
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 1145562

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 3bffde9082f5bb6d1e7fd2598f9acd09199f89e1e0d284d0e51a9d1df5c04ede

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 #1,145,562 on Chainz β†—
Circulating Supply:57,975,028 XPMΒ·at block #6,841,332 Β· updates every 60s
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