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Home/Chain Registry/Block #1,960,826

Block #1,960,826

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/30/2017, 4:08:55 AM Β· Difficulty 10.7422 Β· 4,870,367 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b735821605f7d31a193b40b6cda97206e39f4c5a5b6dd82b1797eded3d077a9b
View on Chainz β†—

Difficulty

10.742244

Transactions

1

Size

199 B

Version

2

Bits

0abe03b8

Nonce

82,498,496

Timestamp

1/30/2017, 4:08:55 AM

Confirmations

4,870,367

Merkle Root

99d7e5c43df0a7c21392d2bf3b35130c8e96ace6780519877180c1d22edb8399
Transactions (1)
Coinbase99d7e5c43df0a7…80c1d22edb8399
1 in β†’ 1 out8.6500 XPM109 B
AMYoBRL4…o1rvRbZU
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.

1.875 Γ— 10⁹⁡(96-digit number)
18759573540292430133…00284816996407636000
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
1.875 Γ— 10⁹⁡(96-digit number)
18759573540292430133…00284816996407635999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.875 Γ— 10⁹⁡(96-digit number)
18759573540292430133…00284816996407636001
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
3.751 Γ— 10⁹⁡(96-digit number)
37519147080584860267…00569633992815271999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.751 Γ— 10⁹⁡(96-digit number)
37519147080584860267…00569633992815272001
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
7.503 Γ— 10⁹⁡(96-digit number)
75038294161169720535…01139267985630543999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.503 Γ— 10⁹⁡(96-digit number)
75038294161169720535…01139267985630544001
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
1.500 Γ— 10⁹⁢(97-digit number)
15007658832233944107…02278535971261087999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.500 Γ— 10⁹⁢(97-digit number)
15007658832233944107…02278535971261088001
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
3.001 Γ— 10⁹⁢(97-digit number)
30015317664467888214…04557071942522175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.001 Γ— 10⁹⁢(97-digit number)
30015317664467888214…04557071942522176001
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 1960826

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 b735821605f7d31a193b40b6cda97206e39f4c5a5b6dd82b1797eded3d077a9b

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 #1,960,826 on Chainz β†—
Circulating Supply:57,893,689 XPMΒ·at block #6,831,192 Β· updates every 60s
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