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Home/Chain Registry/Block #1,880,210

Block #1,880,210

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2016, 6:26:41 PM Β· Difficulty 10.6922 Β· 4,963,048 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ddbabf0a9d5599f3589f5ee1ae1afebaf3faa5a8627bc4e6233906206477a7f9
View on Chainz β†—

Difficulty

10.692224

Transactions

1

Size

199 B

Version

2

Bits

0ab13598

Nonce

1,480,442,793

Timestamp

12/5/2016, 6:26:41 PM

Confirmations

4,963,048

Merkle Root

ebdb921a1d6e3b45496abcf403b5d68423d2c1705b7cec07f452cf6348301fca
Transactions (1)
Coinbaseebdb921a1d6e3b…52cf6348301fca
1 in β†’ 1 out8.7300 XPM109 B
AUFHNBD3…mtQZiooC
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.

2.240 Γ— 10⁹⁴(95-digit number)
22409756488528680042…63669532086563695040
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
2.240 Γ— 10⁹⁴(95-digit number)
22409756488528680042…63669532086563695039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.240 Γ— 10⁹⁴(95-digit number)
22409756488528680042…63669532086563695041
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
4.481 Γ— 10⁹⁴(95-digit number)
44819512977057360085…27339064173127390079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.481 Γ— 10⁹⁴(95-digit number)
44819512977057360085…27339064173127390081
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
8.963 Γ— 10⁹⁴(95-digit number)
89639025954114720171…54678128346254780159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.963 Γ— 10⁹⁴(95-digit number)
89639025954114720171…54678128346254780161
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
1.792 Γ— 10⁹⁡(96-digit number)
17927805190822944034…09356256692509560319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.792 Γ— 10⁹⁡(96-digit number)
17927805190822944034…09356256692509560321
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
3.585 Γ— 10⁹⁡(96-digit number)
35855610381645888068…18712513385019120639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.585 Γ— 10⁹⁡(96-digit number)
35855610381645888068…18712513385019120641
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 1880210

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 ddbabf0a9d5599f3589f5ee1ae1afebaf3faa5a8627bc4e6233906206477a7f9

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 #1,880,210 on Chainz β†—
Circulating Supply:57,990,437 XPMΒ·at block #6,843,257 Β· updates every 60s
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