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Home/Chain Registry/Block #2,879,791

Block #2,879,791

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2018, 7:29:52 PM Β· Difficulty 11.6373 Β· 3,964,229 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06c85f5c2a1d93317fa318b05a0fc8c8a08c493c4479eb76ca8f1092a435934d
View on Chainz β†—

Difficulty

11.637280

Transactions

1

Size

200 B

Version

2

Bits

0ba324c1

Nonce

1,127,586,076

Timestamp

10/13/2018, 7:29:52 PM

Confirmations

3,964,229

Merkle Root

a7a7dd80a615e80f11ec60edcb4f30358f84d524f2b3332f8d2bb367affac17d
Transactions (1)
Coinbasea7a7dd80a615e8…2bb367affac17d
1 in β†’ 1 out7.3700 XPM110 B
ATzvhDN6…HdRg7Wsg
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.

5.850 Γ— 10⁹⁡(96-digit number)
58500442512485853921…52951171491577927680
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
5.850 Γ— 10⁹⁡(96-digit number)
58500442512485853921…52951171491577927679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.850 Γ— 10⁹⁡(96-digit number)
58500442512485853921…52951171491577927681
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
1.170 Γ— 10⁹⁢(97-digit number)
11700088502497170784…05902342983155855359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.170 Γ— 10⁹⁢(97-digit number)
11700088502497170784…05902342983155855361
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
2.340 Γ— 10⁹⁢(97-digit number)
23400177004994341568…11804685966311710719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.340 Γ— 10⁹⁢(97-digit number)
23400177004994341568…11804685966311710721
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
4.680 Γ— 10⁹⁢(97-digit number)
46800354009988683137…23609371932623421439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.680 Γ— 10⁹⁢(97-digit number)
46800354009988683137…23609371932623421441
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
9.360 Γ— 10⁹⁢(97-digit number)
93600708019977366274…47218743865246842879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.360 Γ— 10⁹⁢(97-digit number)
93600708019977366274…47218743865246842881
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
1.872 Γ— 10⁹⁷(98-digit number)
18720141603995473254…94437487730493685759
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 2879791

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 06c85f5c2a1d93317fa318b05a0fc8c8a08c493c4479eb76ca8f1092a435934d

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 #2,879,791 on Chainz β†—
Circulating Supply:57,996,541 XPMΒ·at block #6,844,019 Β· updates every 60s
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