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Block #2,114,414

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/13/2017, 3:28:06 PM Β· Difficulty 10.9000 Β· 4,718,593 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
168c84f25d54e96cb257e999421828714613b61f6c91b1d846444b457974db76
View on Chainz β†—

Difficulty

10.899956

Transactions

2

Size

425 B

Version

2

Bits

0ae66382

Nonce

1,219,967,911

Timestamp

5/13/2017, 3:28:06 PM

Confirmations

4,718,593

Merkle Root

540c9949ef34977c8299340dc1cd53730422ff8c19e18902830068b8465e6eed
Transactions (2)
Coinbase469c27b55b5e12…29057132c1ccda
1 in β†’ 1 out8.4100 XPM109 B
AZMan9oG…ohRx3s56
6718290d583798…f54f672a0612c4
1 in β†’ 2 out3890.3900 XPM226 B
ALNEnoyX…u2cbFnxAAXo7xgdi…w5m2AWXo
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.

5.853 Γ— 10⁹⁴(95-digit number)
58537266584107268349…66740080979174440960
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
5.853 Γ— 10⁹⁴(95-digit number)
58537266584107268349…66740080979174440959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.853 Γ— 10⁹⁴(95-digit number)
58537266584107268349…66740080979174440961
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
1.170 Γ— 10⁹⁡(96-digit number)
11707453316821453669…33480161958348881919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.170 Γ— 10⁹⁡(96-digit number)
11707453316821453669…33480161958348881921
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
2.341 Γ— 10⁹⁡(96-digit number)
23414906633642907339…66960323916697763839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.341 Γ— 10⁹⁡(96-digit number)
23414906633642907339…66960323916697763841
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
4.682 Γ— 10⁹⁡(96-digit number)
46829813267285814679…33920647833395527679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.682 Γ— 10⁹⁡(96-digit number)
46829813267285814679…33920647833395527681
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
9.365 Γ— 10⁹⁡(96-digit number)
93659626534571629359…67841295666791055359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.365 Γ— 10⁹⁡(96-digit number)
93659626534571629359…67841295666791055361
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 2114414

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 168c84f25d54e96cb257e999421828714613b61f6c91b1d846444b457974db76

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 #2,114,414 on Chainz β†—
Circulating Supply:57,908,230 XPMΒ·at block #6,833,006 Β· updates every 60s
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