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Home/Chain Registry/Block #1,691,290

Block #1,691,290

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2016, 12:20:24 PM Β· Difficulty 10.6891 Β· 5,149,532 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b24200e0757b7d62813b65227e88bedeab896724bf11a7e6a3ce7a9b1401d91c
View on Chainz β†—

Difficulty

10.689051

Transactions

1

Size

200 B

Version

2

Bits

0ab065a3

Nonce

1,292,903,088

Timestamp

7/27/2016, 12:20:24 PM

Confirmations

5,149,532

Merkle Root

9a7b2485c54339489dd51283a8a49e51e94aedbef3fc51757a32465d5e90554a
Transactions (1)
Coinbase9a7b2485c54339…32465d5e90554a
1 in β†’ 1 out8.7400 XPM109 B
AR8ennjc…sd4sYFyW
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.

1.084 Γ— 10⁹⁸(99-digit number)
10843668127746337301…15507655958720020480
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
1.084 Γ— 10⁹⁸(99-digit number)
10843668127746337301…15507655958720020479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.084 Γ— 10⁹⁸(99-digit number)
10843668127746337301…15507655958720020481
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
2.168 Γ— 10⁹⁸(99-digit number)
21687336255492674603…31015311917440040959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.168 Γ— 10⁹⁸(99-digit number)
21687336255492674603…31015311917440040961
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
4.337 Γ— 10⁹⁸(99-digit number)
43374672510985349207…62030623834880081919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.337 Γ— 10⁹⁸(99-digit number)
43374672510985349207…62030623834880081921
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
8.674 Γ— 10⁹⁸(99-digit number)
86749345021970698415…24061247669760163839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.674 Γ— 10⁹⁸(99-digit number)
86749345021970698415…24061247669760163841
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
1.734 Γ— 10⁹⁹(100-digit number)
17349869004394139683…48122495339520327679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.734 Γ— 10⁹⁹(100-digit number)
17349869004394139683…48122495339520327681
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 1691290

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 b24200e0757b7d62813b65227e88bedeab896724bf11a7e6a3ce7a9b1401d91c

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 #1,691,290 on Chainz β†—
Circulating Supply:57,970,929 XPMΒ·at block #6,840,821 Β· updates every 60s
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