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Home/Chain Registry/Block #2,853,103

Block #2,853,103

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2018, 9:21:03 AM Β· Difficulty 11.7178 Β· 3,990,511 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8d65ec576e535ca60d6e25727a942a608c23d901e1b7d895afd1029b8a65056
View on Chainz β†—

Difficulty

11.717821

Transactions

1

Size

202 B

Version

2

Bits

0bb7c31d

Nonce

921,324,364

Timestamp

9/24/2018, 9:21:03 AM

Confirmations

3,990,511

Merkle Root

fc855999f23582d1f995413f99e2e913829bd293f365051e8665b7a88185e65f
Transactions (1)
Coinbasefc855999f23582…65b7a88185e65f
1 in β†’ 1 out7.2700 XPM110 B
AJ5v2bFd…t9bTYZGx
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.

3.730 Γ— 10⁹⁸(99-digit number)
37303724287869482175…17945257231869870080
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
3.730 Γ— 10⁹⁸(99-digit number)
37303724287869482175…17945257231869870079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.730 Γ— 10⁹⁸(99-digit number)
37303724287869482175…17945257231869870081
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
7.460 Γ— 10⁹⁸(99-digit number)
74607448575738964351…35890514463739740159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.460 Γ— 10⁹⁸(99-digit number)
74607448575738964351…35890514463739740161
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
1.492 Γ— 10⁹⁹(100-digit number)
14921489715147792870…71781028927479480319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.492 Γ— 10⁹⁹(100-digit number)
14921489715147792870…71781028927479480321
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
2.984 Γ— 10⁹⁹(100-digit number)
29842979430295585740…43562057854958960639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.984 Γ— 10⁹⁹(100-digit number)
29842979430295585740…43562057854958960641
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
5.968 Γ— 10⁹⁹(100-digit number)
59685958860591171481…87124115709917921279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.968 Γ— 10⁹⁹(100-digit number)
59685958860591171481…87124115709917921281
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
1.193 Γ— 10¹⁰⁰(101-digit number)
11937191772118234296…74248231419835842559
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 2853103

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 f8d65ec576e535ca60d6e25727a942a608c23d901e1b7d895afd1029b8a65056

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 #2,853,103 on Chainz β†—
Circulating Supply:57,993,276 XPMΒ·at block #6,843,613 Β· updates every 60s
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