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Home/Chain Registry/Block #1,680,605

Block #1,680,605

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2016, 8:42:18 PM Β· Difficulty 10.7087 Β· 5,160,541 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2d290993f44213c2289a99de0e35800cb5ff7e555043a0442a7c02eef40f5f38
View on Chainz β†—

Difficulty

10.708727

Transactions

1

Size

200 B

Version

2

Bits

0ab56f26

Nonce

1,438,443,651

Timestamp

7/19/2016, 8:42:18 PM

Confirmations

5,160,541

Merkle Root

42921e432444d2aaa46ce2dc271d1a520161e0f725cc74cea3e0a260c678c309
Transactions (1)
Coinbase42921e432444d2…e0a260c678c309
1 in β†’ 1 out8.7100 XPM109 B
AT4Hiyg6…Fo3n2B8E
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.

1.052 Γ— 10⁹⁷(98-digit number)
10527170251408029168…33078996748540385280
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
1.052 Γ— 10⁹⁷(98-digit number)
10527170251408029168…33078996748540385279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.052 Γ— 10⁹⁷(98-digit number)
10527170251408029168…33078996748540385281
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
2.105 Γ— 10⁹⁷(98-digit number)
21054340502816058337…66157993497080770559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.105 Γ— 10⁹⁷(98-digit number)
21054340502816058337…66157993497080770561
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
4.210 Γ— 10⁹⁷(98-digit number)
42108681005632116674…32315986994161541119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.210 Γ— 10⁹⁷(98-digit number)
42108681005632116674…32315986994161541121
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
8.421 Γ— 10⁹⁷(98-digit number)
84217362011264233348…64631973988323082239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.421 Γ— 10⁹⁷(98-digit number)
84217362011264233348…64631973988323082241
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
1.684 Γ— 10⁹⁸(99-digit number)
16843472402252846669…29263947976646164479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.684 Γ— 10⁹⁸(99-digit number)
16843472402252846669…29263947976646164481
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 1680605

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 2d290993f44213c2289a99de0e35800cb5ff7e555043a0442a7c02eef40f5f38

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 #1,680,605 on Chainz β†—
Circulating Supply:57,973,530 XPMΒ·at block #6,841,145 Β· updates every 60s
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