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Home/Chain Registry/Block #2,913,466

Block #2,913,466

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2018, 8:45:20 AM Β· Difficulty 11.4953 Β· 3,929,818 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9dfffd8941675cbafa1d4f2ffb53bfecd720c7d03ee9508dd2414dd1b11b636b
View on Chainz β†—

Difficulty

11.495295

Transactions

1

Size

199 B

Version

2

Bits

0b7ecbac

Nonce

510,447,202

Timestamp

11/7/2018, 8:45:20 AM

Confirmations

3,929,818

Merkle Root

527c4349bb96f8cf6a5c8365a7058770b228b8e0860a1583f3141f1bde17f5ab
Transactions (1)
Coinbase527c4349bb96f8…141f1bde17f5ab
1 in β†’ 1 out7.5600 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.055 Γ— 10⁹²(93-digit number)
30557629114463720691…49556471452609318400
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
3.055 Γ— 10⁹²(93-digit number)
30557629114463720691…49556471452609318399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.055 Γ— 10⁹²(93-digit number)
30557629114463720691…49556471452609318401
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
6.111 Γ— 10⁹²(93-digit number)
61115258228927441383…99112942905218636799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.111 Γ— 10⁹²(93-digit number)
61115258228927441383…99112942905218636801
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
1.222 Γ— 10⁹³(94-digit number)
12223051645785488276…98225885810437273599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.222 Γ— 10⁹³(94-digit number)
12223051645785488276…98225885810437273601
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
2.444 Γ— 10⁹³(94-digit number)
24446103291570976553…96451771620874547199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.444 Γ— 10⁹³(94-digit number)
24446103291570976553…96451771620874547201
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
4.889 Γ— 10⁹³(94-digit number)
48892206583141953106…92903543241749094399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.889 Γ— 10⁹³(94-digit number)
48892206583141953106…92903543241749094401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.778 Γ— 10⁹³(94-digit number)
97784413166283906213…85807086483498188799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2913466

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 9dfffd8941675cbafa1d4f2ffb53bfecd720c7d03ee9508dd2414dd1b11b636b

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 #2,913,466 on Chainz β†—
Circulating Supply:57,990,645 XPMΒ·at block #6,843,283 Β· updates every 60s
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