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Home/Chain Registry/Block #2,271,395

Block #2,271,395

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 5:30:33 AM Β· Difficulty 10.9536 Β· 4,568,643 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
be3247cc42b9b865ee9ad507a81a446ba3b1b61468f04fd4be9eeacfb7d1b06c
View on Chainz β†—

Difficulty

10.953630

Transactions

1

Size

199 B

Version

2

Bits

0af42113

Nonce

1,526,085,056

Timestamp

8/28/2017, 5:30:33 AM

Confirmations

4,568,643

Merkle Root

01bf9c616116d24387f93c39f67ecaa0cb1791a13cda2912387f650f001fa5fc
Transactions (1)
Coinbase01bf9c616116d2…7f650f001fa5fc
1 in β†’ 1 out8.3200 XPM110 B
AX5QmyAu…A4mbNmhs
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.

8.483 Γ— 10⁹²(93-digit number)
84838016715015550140…18406921518320360320
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
8.483 Γ— 10⁹²(93-digit number)
84838016715015550140…18406921518320360319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.483 Γ— 10⁹²(93-digit number)
84838016715015550140…18406921518320360321
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
1.696 Γ— 10⁹³(94-digit number)
16967603343003110028…36813843036640720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.696 Γ— 10⁹³(94-digit number)
16967603343003110028…36813843036640720641
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
3.393 Γ— 10⁹³(94-digit number)
33935206686006220056…73627686073281441279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.393 Γ— 10⁹³(94-digit number)
33935206686006220056…73627686073281441281
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
6.787 Γ— 10⁹³(94-digit number)
67870413372012440112…47255372146562882559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.787 Γ— 10⁹³(94-digit number)
67870413372012440112…47255372146562882561
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
1.357 Γ— 10⁹⁴(95-digit number)
13574082674402488022…94510744293125765119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.357 Γ— 10⁹⁴(95-digit number)
13574082674402488022…94510744293125765121
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 2271395

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 be3247cc42b9b865ee9ad507a81a446ba3b1b61468f04fd4be9eeacfb7d1b06c

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 #2,271,395 on Chainz β†—
Circulating Supply:57,964,618 XPMΒ·at block #6,840,037 Β· updates every 60s
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