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Home/Chain Registry/Block #2,770,365

Block #2,770,365

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2018, 1:41:32 PM Β· Difficulty 11.6583 Β· 4,072,712 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9fb120a4c0de688b509cd79c659693eb435d9976b2d810c878b2941ae9086fc4
View on Chainz β†—

Difficulty

11.658337

Transactions

1

Size

200 B

Version

2

Bits

0ba888ce

Nonce

338,049,015

Timestamp

7/29/2018, 1:41:32 PM

Confirmations

4,072,712

Merkle Root

f1b71401bd68796be838f0b3daef214d2a011ea2f32fc812d905f754ba7899f2
Transactions (1)
Coinbasef1b71401bd6879…05f754ba7899f2
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.192 Γ— 10⁹⁴(95-digit number)
11928715487448296284…44176836170250421900
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
1.192 Γ— 10⁹⁴(95-digit number)
11928715487448296284…44176836170250421899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.192 Γ— 10⁹⁴(95-digit number)
11928715487448296284…44176836170250421901
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
2.385 Γ— 10⁹⁴(95-digit number)
23857430974896592569…88353672340500843799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.385 Γ— 10⁹⁴(95-digit number)
23857430974896592569…88353672340500843801
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
4.771 Γ— 10⁹⁴(95-digit number)
47714861949793185138…76707344681001687599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.771 Γ— 10⁹⁴(95-digit number)
47714861949793185138…76707344681001687601
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
9.542 Γ— 10⁹⁴(95-digit number)
95429723899586370277…53414689362003375199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.542 Γ— 10⁹⁴(95-digit number)
95429723899586370277…53414689362003375201
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
1.908 Γ— 10⁹⁡(96-digit number)
19085944779917274055…06829378724006750399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.908 Γ— 10⁹⁡(96-digit number)
19085944779917274055…06829378724006750401
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
3.817 Γ— 10⁹⁡(96-digit number)
38171889559834548111…13658757448013500799
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 2770365

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 9fb120a4c0de688b509cd79c659693eb435d9976b2d810c878b2941ae9086fc4

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 #2,770,365 on Chainz β†—
Circulating Supply:57,988,976 XPMΒ·at block #6,843,076 Β· updates every 60s
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