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Home/Chain Registry/Block #2,177,885

Block #2,177,885

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 7:32:25 PM Β· Difficulty 10.9244 Β· 4,652,646 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0291f29fa9c5334f36e1ed5de35e43bce5daab6fb533858992cb61ee30fef3db
View on Chainz β†—

Difficulty

10.924405

Transactions

2

Size

49.95 KB

Version

2

Bits

0aeca5ca

Nonce

94,333,791

Timestamp

6/25/2017, 7:32:25 PM

Confirmations

4,652,646

Merkle Root

71b98c967743dcadc596ddd9ed931c8d6406e31604bc21fb83007e3cceedeaeb
Transactions (2)
Coinbased94560ded5fa8d…37a3c1a71e14e3
1 in β†’ 1 out8.8800 XPM109 B
AecDK7Hb…d6CdkeFL
22f1868c7fbc76…ba933e80f33de0
344 in β†’ 1 out46189.0440 XPM49.76 KB
ALpEhJp7…SkLEaPuv
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.

3.128 Γ— 10⁹⁢(97-digit number)
31285329883766913400…52698035854328463360
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
3.128 Γ— 10⁹⁢(97-digit number)
31285329883766913400…52698035854328463359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.128 Γ— 10⁹⁢(97-digit number)
31285329883766913400…52698035854328463361
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
6.257 Γ— 10⁹⁢(97-digit number)
62570659767533826801…05396071708656926719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.257 Γ— 10⁹⁢(97-digit number)
62570659767533826801…05396071708656926721
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
1.251 Γ— 10⁹⁷(98-digit number)
12514131953506765360…10792143417313853439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12514131953506765360…10792143417313853441
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
2.502 Γ— 10⁹⁷(98-digit number)
25028263907013530720…21584286834627706879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.502 Γ— 10⁹⁷(98-digit number)
25028263907013530720…21584286834627706881
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
5.005 Γ— 10⁹⁷(98-digit number)
50056527814027061440…43168573669255413759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.005 Γ— 10⁹⁷(98-digit number)
50056527814027061440…43168573669255413761
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
1.001 Γ— 10⁹⁸(99-digit number)
10011305562805412288…86337147338510827519
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 2177885

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 0291f29fa9c5334f36e1ed5de35e43bce5daab6fb533858992cb61ee30fef3db

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 #2,177,885 on Chainz β†—
Circulating Supply:57,888,501 XPMΒ·at block #6,830,530 Β· updates every 60s
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