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Home/Chain Registry/Block #2,056,965

Block #2,056,965

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2017, 3:03:58 PM Β· Difficulty 10.8265 Β· 4,788,683 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0e74d1a19d4823037e136b2129fcd93dc1d48703144e5b349e4a6f91a37a6153
View on Chainz β†—

Difficulty

10.826485

Transactions

1

Size

198 B

Version

2

Bits

0ad39485

Nonce

1,047,026,782

Timestamp

4/5/2017, 3:03:58 PM

Confirmations

4,788,683

Merkle Root

6b6c73381d261d1a556bf770046324fabe186661fe2bc694a99560561ecae565
Transactions (1)
Coinbase6b6c73381d261d…9560561ecae565
1 in β†’ 1 out8.5200 XPM109 B
AYEqsXk9…SihhLnV9
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.

1.999 Γ— 10⁹³(94-digit number)
19990730975848692798…97946500948094929290
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
1.999 Γ— 10⁹³(94-digit number)
19990730975848692798…97946500948094929289
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.999 Γ— 10⁹³(94-digit number)
19990730975848692798…97946500948094929291
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
3.998 Γ— 10⁹³(94-digit number)
39981461951697385596…95893001896189858579
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.998 Γ— 10⁹³(94-digit number)
39981461951697385596…95893001896189858581
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
7.996 Γ— 10⁹³(94-digit number)
79962923903394771193…91786003792379717159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.996 Γ— 10⁹³(94-digit number)
79962923903394771193…91786003792379717161
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
1.599 Γ— 10⁹⁴(95-digit number)
15992584780678954238…83572007584759434319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.599 Γ— 10⁹⁴(95-digit number)
15992584780678954238…83572007584759434321
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
3.198 Γ— 10⁹⁴(95-digit number)
31985169561357908477…67144015169518868639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.198 Γ— 10⁹⁴(95-digit number)
31985169561357908477…67144015169518868641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.397 Γ— 10⁹⁴(95-digit number)
63970339122715816954…34288030339037737279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2056965

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 0e74d1a19d4823037e136b2129fcd93dc1d48703144e5b349e4a6f91a37a6153

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 #2,056,965 on Chainz β†—
Circulating Supply:58,009,633 XPMΒ·at block #6,845,647 Β· updates every 60s
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