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Home/Chain Registry/Block #1,634,850

Block #1,634,850

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/19/2016, 12:39:21 AM Β· Difficulty 10.6164 Β· 5,190,164 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
784991c85895f1154c57783c7d677622060aa78f2d53e8ceb46c3a25c8a4765c
View on Chainz β†—

Difficulty

10.616422

Transactions

2

Size

2.01 KB

Version

2

Bits

0a9dcddc

Nonce

660,046,743

Timestamp

6/19/2016, 12:39:21 AM

Confirmations

5,190,164

Merkle Root

873e123cb6b1a8d1f927c919c05d286f2d46eb7cf9f39f32dfc62400f5b5ff53
Transactions (2)
Coinbase2ae8c75139143c…9ccf4828a00aac
1 in β†’ 1 out8.8800 XPM110 B
AQsNVb1r…GuFjyudS
0c5877cc26daa1…8527c7d9186dc9
12 in β†’ 2 out417.5800 XPM1.82 KB
ALZ1fV2B…NDTZhmFFAcDhjHA9…ebukETHz
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.

7.092 Γ— 10⁹⁢(97-digit number)
70924648221023273292…98543858232189378560
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
7.092 Γ— 10⁹⁢(97-digit number)
70924648221023273292…98543858232189378559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.092 Γ— 10⁹⁢(97-digit number)
70924648221023273292…98543858232189378561
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
1.418 Γ— 10⁹⁷(98-digit number)
14184929644204654658…97087716464378757119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.418 Γ— 10⁹⁷(98-digit number)
14184929644204654658…97087716464378757121
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
2.836 Γ— 10⁹⁷(98-digit number)
28369859288409309317…94175432928757514239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.836 Γ— 10⁹⁷(98-digit number)
28369859288409309317…94175432928757514241
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
5.673 Γ— 10⁹⁷(98-digit number)
56739718576818618634…88350865857515028479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.673 Γ— 10⁹⁷(98-digit number)
56739718576818618634…88350865857515028481
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
1.134 Γ— 10⁹⁸(99-digit number)
11347943715363723726…76701731715030056959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.134 Γ— 10⁹⁸(99-digit number)
11347943715363723726…76701731715030056961
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 1634850

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 784991c85895f1154c57783c7d677622060aa78f2d53e8ceb46c3a25c8a4765c

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 #1,634,850 on Chainz β†—
Circulating Supply:57,844,197 XPMΒ·at block #6,825,013 Β· updates every 60s
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