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Home/Chain Registry/Block #1,120,790

Block #1,120,790

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2015, 9:37:41 AM Β· Difficulty 10.9362 Β· 5,680,607 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a15e7b7519e9c2cf8504f17bec7e9d5950a9939b1a7d45e39fee69ee4576f4ef
View on Chainz β†—

Difficulty

10.936153

Transactions

1

Size

200 B

Version

2

Bits

0aefa7b4

Nonce

1,307,827,549

Timestamp

6/21/2015, 9:37:41 AM

Confirmations

5,680,607

Merkle Root

787d6d769ec566219d9e3f0f6ea77c876425474a9ea7ba72f39e1accce4e724b
Transactions (1)
Coinbase787d6d769ec566…9e1accce4e724b
1 in β†’ 1 out8.3500 XPM109 B
Aaxj2SBU…iHAza6RG
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.

1.570 Γ— 10⁹⁸(99-digit number)
15706402511418316957…68867228589113999360
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
1.570 Γ— 10⁹⁸(99-digit number)
15706402511418316957…68867228589113999359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.570 Γ— 10⁹⁸(99-digit number)
15706402511418316957…68867228589113999361
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
3.141 Γ— 10⁹⁸(99-digit number)
31412805022836633915…37734457178227998719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.141 Γ— 10⁹⁸(99-digit number)
31412805022836633915…37734457178227998721
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
6.282 Γ— 10⁹⁸(99-digit number)
62825610045673267830…75468914356455997439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.282 Γ— 10⁹⁸(99-digit number)
62825610045673267830…75468914356455997441
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
1.256 Γ— 10⁹⁹(100-digit number)
12565122009134653566…50937828712911994879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.256 Γ— 10⁹⁹(100-digit number)
12565122009134653566…50937828712911994881
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
2.513 Γ— 10⁹⁹(100-digit number)
25130244018269307132…01875657425823989759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.513 Γ— 10⁹⁹(100-digit number)
25130244018269307132…01875657425823989761
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 1120790

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 a15e7b7519e9c2cf8504f17bec7e9d5950a9939b1a7d45e39fee69ee4576f4ef

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 #1,120,790 on Chainz β†—
Circulating Supply:57,655,244 XPMΒ·at block #6,801,396 Β· updates every 60s
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