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Home/Chain Registry/Block #1,285,874

Block #1,285,874

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/17/2015, 7:46:11 AM Β· Difficulty 10.8446 Β· 5,540,720 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e1be96e1d04a02e814d450c8124e88907fb6a62590dba021f86492e3b09a904
View on Chainz β†—

Difficulty

10.844624

Transactions

1

Size

202 B

Version

2

Bits

0ad8394b

Nonce

199,917,194

Timestamp

10/17/2015, 7:46:11 AM

Confirmations

5,540,720

Merkle Root

d6560c53382acf6638c5eab5a216aa73cc1eea8aa69466355a1ea775a35311d5
Transactions (1)
Coinbased6560c53382acf…1ea775a35311d5
1 in β†’ 1 out8.4900 XPM110 B
ALGjsD9y…WCTWDf5v
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.

2.626 Γ— 10⁹⁸(99-digit number)
26269899252427425763…46378870429848043520
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
2.626 Γ— 10⁹⁸(99-digit number)
26269899252427425763…46378870429848043519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.626 Γ— 10⁹⁸(99-digit number)
26269899252427425763…46378870429848043521
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
5.253 Γ— 10⁹⁸(99-digit number)
52539798504854851527…92757740859696087039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.253 Γ— 10⁹⁸(99-digit number)
52539798504854851527…92757740859696087041
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
1.050 Γ— 10⁹⁹(100-digit number)
10507959700970970305…85515481719392174079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.050 Γ— 10⁹⁹(100-digit number)
10507959700970970305…85515481719392174081
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
2.101 Γ— 10⁹⁹(100-digit number)
21015919401941940611…71030963438784348159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.101 Γ— 10⁹⁹(100-digit number)
21015919401941940611…71030963438784348161
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
4.203 Γ— 10⁹⁹(100-digit number)
42031838803883881222…42061926877568696319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.203 Γ— 10⁹⁹(100-digit number)
42031838803883881222…42061926877568696321
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 1285874

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 3e1be96e1d04a02e814d450c8124e88907fb6a62590dba021f86492e3b09a904

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 #1,285,874 on Chainz β†—
Circulating Supply:57,856,904 XPMΒ·at block #6,826,593 Β· updates every 60s
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