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Home/Chain Registry/Block #1,710,914

Block #1,710,914

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/10/2016, 4:28:22 PM Β· Difficulty 10.6376 Β· 5,133,142 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
644ec799a70e6554de957576641a8fa301b497267ddd8a3cd0741a7cd9c383b0
View on Chainz β†—

Difficulty

10.637623

Transactions

1

Size

200 B

Version

2

Bits

0aa33b4b

Nonce

169,876,472

Timestamp

8/10/2016, 4:28:22 PM

Confirmations

5,133,142

Merkle Root

3f1c4ff8dcfd322db9e9c33fa81d2e8bb2ff736e9cffacabbbdb74e0db6ef82e
Transactions (1)
Coinbase3f1c4ff8dcfd32…db74e0db6ef82e
1 in β†’ 1 out8.8200 XPM110 B
AannWmGr…Xzrhwumq
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.

7.417 Γ— 10⁹³(94-digit number)
74170612400125107831…78556589499684038800
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
7.417 Γ— 10⁹³(94-digit number)
74170612400125107831…78556589499684038799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.417 Γ— 10⁹³(94-digit number)
74170612400125107831…78556589499684038801
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
1.483 Γ— 10⁹⁴(95-digit number)
14834122480025021566…57113178999368077599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.483 Γ— 10⁹⁴(95-digit number)
14834122480025021566…57113178999368077601
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
2.966 Γ— 10⁹⁴(95-digit number)
29668244960050043132…14226357998736155199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.966 Γ— 10⁹⁴(95-digit number)
29668244960050043132…14226357998736155201
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
5.933 Γ— 10⁹⁴(95-digit number)
59336489920100086264…28452715997472310399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.933 Γ— 10⁹⁴(95-digit number)
59336489920100086264…28452715997472310401
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
1.186 Γ— 10⁹⁡(96-digit number)
11867297984020017252…56905431994944620799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.186 Γ— 10⁹⁡(96-digit number)
11867297984020017252…56905431994944620801
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 1710914

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 644ec799a70e6554de957576641a8fa301b497267ddd8a3cd0741a7cd9c383b0

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 #1,710,914 on Chainz β†—
Circulating Supply:57,996,819 XPMΒ·at block #6,844,055 Β· updates every 60s
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