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Home/Chain Registry/Block #2,116,842

Block #2,116,842

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2017, 3:56:24 AM Β· Difficulty 10.9047 Β· 4,727,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c345ea6171857bb0c829c325cfc0b21f597f02883d7e6828c9f7a373863eaf0c
View on Chainz β†—

Difficulty

10.904678

Transactions

1

Size

200 B

Version

2

Bits

0ae798fd

Nonce

866,501,560

Timestamp

5/15/2017, 3:56:24 AM

Confirmations

4,727,193

Merkle Root

e1006c94640bd74c91c400b1ea3c8e0933a716e3d685859f5c8bdaf0c3e2931b
Transactions (1)
Coinbasee1006c94640bd7…8bdaf0c3e2931b
1 in β†’ 1 out8.4000 XPM110 B
AdStkTLH…TjcPnpVD
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.

2.130 Γ— 10⁹⁡(96-digit number)
21300324666877005669…24699803014122142080
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
2.130 Γ— 10⁹⁡(96-digit number)
21300324666877005669…24699803014122142079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.130 Γ— 10⁹⁡(96-digit number)
21300324666877005669…24699803014122142081
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
4.260 Γ— 10⁹⁡(96-digit number)
42600649333754011338…49399606028244284159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.260 Γ— 10⁹⁡(96-digit number)
42600649333754011338…49399606028244284161
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
8.520 Γ— 10⁹⁡(96-digit number)
85201298667508022677…98799212056488568319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.520 Γ— 10⁹⁡(96-digit number)
85201298667508022677…98799212056488568321
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
1.704 Γ— 10⁹⁢(97-digit number)
17040259733501604535…97598424112977136639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.704 Γ— 10⁹⁢(97-digit number)
17040259733501604535…97598424112977136641
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
3.408 Γ— 10⁹⁢(97-digit number)
34080519467003209070…95196848225954273279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.408 Γ— 10⁹⁢(97-digit number)
34080519467003209070…95196848225954273281
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 2116842

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 c345ea6171857bb0c829c325cfc0b21f597f02883d7e6828c9f7a373863eaf0c

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 #2,116,842 on Chainz β†—
Circulating Supply:57,996,657 XPMΒ·at block #6,844,034 Β· updates every 60s
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