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Home/Chain Registry/Block #2,295,927

Block #2,295,927

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2017, 12:17:11 PM Β· Difficulty 10.9511 Β· 4,543,945 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
116001c1505d3320c9067c4c48c8ec22baccf64fdbdf1c1127ebac19577eec62
View on Chainz β†—

Difficulty

10.951080

Transactions

2

Size

2.58 KB

Version

2

Bits

0af37a00

Nonce

1,741,207,668

Timestamp

9/14/2017, 12:17:11 PM

Confirmations

4,543,945

Merkle Root

078450a76657440e6a158a3f735d802cacebb923e6808cb5115099cae0a9b432
Transactions (2)
Coinbase1ced967e19dc64…2c4bd5c4030ecc
1 in β†’ 1 out8.3600 XPM110 B
ALZ2yMoR…QyWCsoaB
982124389fbe9e…2c23b323141db9
16 in β†’ 2 out4193.8595 XPM2.39 KB
AViBaKwf…3Xk3qwK8AcfqDnSg…i1vSHQjb
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.

1.335 Γ— 10⁹⁡(96-digit number)
13355186511730616881…04640918957783159040
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
1.335 Γ— 10⁹⁡(96-digit number)
13355186511730616881…04640918957783159039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.335 Γ— 10⁹⁡(96-digit number)
13355186511730616881…04640918957783159041
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
2.671 Γ— 10⁹⁡(96-digit number)
26710373023461233763…09281837915566318079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.671 Γ— 10⁹⁡(96-digit number)
26710373023461233763…09281837915566318081
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
5.342 Γ— 10⁹⁡(96-digit number)
53420746046922467527…18563675831132636159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.342 Γ— 10⁹⁡(96-digit number)
53420746046922467527…18563675831132636161
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
1.068 Γ— 10⁹⁢(97-digit number)
10684149209384493505…37127351662265272319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.068 Γ— 10⁹⁢(97-digit number)
10684149209384493505…37127351662265272321
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
2.136 Γ— 10⁹⁢(97-digit number)
21368298418768987011…74254703324530544639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.136 Γ— 10⁹⁢(97-digit number)
21368298418768987011…74254703324530544641
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 2295927

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 116001c1505d3320c9067c4c48c8ec22baccf64fdbdf1c1127ebac19577eec62

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 #2,295,927 on Chainz β†—
Circulating Supply:57,963,276 XPMΒ·at block #6,839,871 Β· updates every 60s
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