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Home/Chain Registry/Block #2,072,260

Block #2,072,260

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/15/2017, 4:04:55 PM Β· Difficulty 10.8534 Β· 4,760,303 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16a3bd78d291f757474c258dffbca82b84afb239b0ec0275689a28697c77e6ed
View on Chainz β†—

Difficulty

10.853444

Transactions

1

Size

200 B

Version

2

Bits

0ada7b53

Nonce

1,139,795,813

Timestamp

4/15/2017, 4:04:55 PM

Confirmations

4,760,303

Merkle Root

588274b23dd9e77e9fe76e2fba9748e3ed442a08980d3c7c4c91db7b3cf91664
Transactions (1)
Coinbase588274b23dd9e7…91db7b3cf91664
1 in β†’ 1 out8.4800 XPM109 B
AaDwjUXy…iWihc2jK
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.

2.659 Γ— 10⁹⁢(97-digit number)
26592929811314285594…49169816946186104320
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
2.659 Γ— 10⁹⁢(97-digit number)
26592929811314285594…49169816946186104319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.659 Γ— 10⁹⁢(97-digit number)
26592929811314285594…49169816946186104321
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
5.318 Γ— 10⁹⁢(97-digit number)
53185859622628571189…98339633892372208639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.318 Γ— 10⁹⁢(97-digit number)
53185859622628571189…98339633892372208641
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
1.063 Γ— 10⁹⁷(98-digit number)
10637171924525714237…96679267784744417279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.063 Γ— 10⁹⁷(98-digit number)
10637171924525714237…96679267784744417281
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
2.127 Γ— 10⁹⁷(98-digit number)
21274343849051428475…93358535569488834559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.127 Γ— 10⁹⁷(98-digit number)
21274343849051428475…93358535569488834561
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
4.254 Γ— 10⁹⁷(98-digit number)
42548687698102856951…86717071138977669119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.254 Γ— 10⁹⁷(98-digit number)
42548687698102856951…86717071138977669121
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 2072260

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 16a3bd78d291f757474c258dffbca82b84afb239b0ec0275689a28697c77e6ed

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 #2,072,260 on Chainz β†—
Circulating Supply:57,904,661 XPMΒ·at block #6,832,562 Β· updates every 60s
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