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Home/Chain Registry/Block #3,241,271

Block #3,241,271

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/26/2019, 4:21:09 AM Β· Difficulty 11.0039 Β· 3,602,473 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
974a765ee7bc38ff8135c874dd5dd000751d68c41cedb4834910bb7638af78ac
View on Chainz β†—

Difficulty

11.003918

Transactions

2

Size

393 B

Version

2

Bits

0b0100bd

Nonce

861,800,132

Timestamp

6/26/2019, 4:21:09 AM

Confirmations

3,602,473

Merkle Root

a5813f83a57223793802cd292b4d05b7e88cdd50b9149ab7d310cc26e8e97a53
Transactions (2)
Coinbase0c748f23aaf70e…0970da2859a653
1 in β†’ 1 out8.2600 XPM110 B
ARbm48qR…9xQc8DBX
eff363fe408043…84575e00fd0c38
1 in β†’ 1 out140.1132 XPM192 B
AXXGfizT…aeWx1Cui
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.

7.402 Γ— 10⁹⁢(97-digit number)
74023270759814602023…43643139084364743040
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
7.402 Γ— 10⁹⁢(97-digit number)
74023270759814602023…43643139084364743039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.402 Γ— 10⁹⁢(97-digit number)
74023270759814602023…43643139084364743041
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
1.480 Γ— 10⁹⁷(98-digit number)
14804654151962920404…87286278168729486079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.480 Γ— 10⁹⁷(98-digit number)
14804654151962920404…87286278168729486081
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
2.960 Γ— 10⁹⁷(98-digit number)
29609308303925840809…74572556337458972159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.960 Γ— 10⁹⁷(98-digit number)
29609308303925840809…74572556337458972161
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
5.921 Γ— 10⁹⁷(98-digit number)
59218616607851681618…49145112674917944319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.921 Γ— 10⁹⁷(98-digit number)
59218616607851681618…49145112674917944321
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
1.184 Γ— 10⁹⁸(99-digit number)
11843723321570336323…98290225349835888639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.184 Γ— 10⁹⁸(99-digit number)
11843723321570336323…98290225349835888641
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
2.368 Γ— 10⁹⁸(99-digit number)
23687446643140672647…96580450699671777279
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 3241271

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 974a765ee7bc38ff8135c874dd5dd000751d68c41cedb4834910bb7638af78ac

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 #3,241,271 on Chainz β†—
Circulating Supply:57,994,322 XPMΒ·at block #6,843,743 Β· updates every 60s
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