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Home/Chain Registry/Block #2,640,857

Block #2,640,857

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 3:42:03 AM Β· Difficulty 11.5982 Β· 4,191,786 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0deb5de8e6fd83b811157095767024c0686b41d9b49e0dd6a3f67f47a256a3ba
View on Chainz β†—

Difficulty

11.598218

Transactions

1

Size

200 B

Version

2

Bits

0b9924cf

Nonce

516,531,223

Timestamp

5/1/2018, 3:42:03 AM

Confirmations

4,191,786

Merkle Root

f3319d37e490f85345f9555206755aa0070bd7b6630b8c28c0c8847a5481d18a
Transactions (1)
Coinbasef3319d37e490f8…c8847a5481d18a
1 in β†’ 1 out7.4200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.153 Γ— 10⁹⁡(96-digit number)
11534325497518096943…35486972382069381120
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
1.153 Γ— 10⁹⁡(96-digit number)
11534325497518096943…35486972382069381119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.153 Γ— 10⁹⁡(96-digit number)
11534325497518096943…35486972382069381121
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
2.306 Γ— 10⁹⁡(96-digit number)
23068650995036193886…70973944764138762239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.306 Γ— 10⁹⁡(96-digit number)
23068650995036193886…70973944764138762241
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
4.613 Γ— 10⁹⁡(96-digit number)
46137301990072387773…41947889528277524479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.613 Γ— 10⁹⁡(96-digit number)
46137301990072387773…41947889528277524481
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
9.227 Γ— 10⁹⁡(96-digit number)
92274603980144775546…83895779056555048959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.227 Γ— 10⁹⁡(96-digit number)
92274603980144775546…83895779056555048961
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
1.845 Γ— 10⁹⁢(97-digit number)
18454920796028955109…67791558113110097919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.845 Γ— 10⁹⁢(97-digit number)
18454920796028955109…67791558113110097921
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
3.690 Γ— 10⁹⁢(97-digit number)
36909841592057910218…35583116226220195839
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 2640857

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 0deb5de8e6fd83b811157095767024c0686b41d9b49e0dd6a3f67f47a256a3ba

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 #2,640,857 on Chainz β†—
Circulating Supply:57,905,294 XPMΒ·at block #6,832,642 Β· updates every 60s
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