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Home/Chain Registry/Block #2,151,804

Block #2,151,804

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2017, 3:23:21 PM Β· Difficulty 10.9003 Β· 4,675,294 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c48f848ee13eae1ae51a011b1943cc6755ea26c3ff8ba1dbbc205b2d71f47c6a
View on Chainz β†—

Difficulty

10.900281

Transactions

1

Size

199 B

Version

2

Bits

0ae678d1

Nonce

1,241,113,648

Timestamp

6/8/2017, 3:23:21 PM

Confirmations

4,675,294

Merkle Root

02d40656e6e996f1f37a1b635946582baa6d84612d3062fd179f9c81ba76ee02
Transactions (1)
Coinbase02d40656e6e996…9f9c81ba76ee02
1 in β†’ 1 out8.4000 XPM109 B
AQU6MdVk…ZNu2dCGL
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.

3.096 Γ— 10⁹⁴(95-digit number)
30966029499635203983…82913269942284474560
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
3.096 Γ— 10⁹⁴(95-digit number)
30966029499635203983…82913269942284474559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.096 Γ— 10⁹⁴(95-digit number)
30966029499635203983…82913269942284474561
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
6.193 Γ— 10⁹⁴(95-digit number)
61932058999270407967…65826539884568949119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.193 Γ— 10⁹⁴(95-digit number)
61932058999270407967…65826539884568949121
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
1.238 Γ— 10⁹⁡(96-digit number)
12386411799854081593…31653079769137898239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.238 Γ— 10⁹⁡(96-digit number)
12386411799854081593…31653079769137898241
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
2.477 Γ— 10⁹⁡(96-digit number)
24772823599708163187…63306159538275796479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.477 Γ— 10⁹⁡(96-digit number)
24772823599708163187…63306159538275796481
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
4.954 Γ— 10⁹⁡(96-digit number)
49545647199416326374…26612319076551592959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.954 Γ— 10⁹⁡(96-digit number)
49545647199416326374…26612319076551592961
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
9.909 Γ— 10⁹⁡(96-digit number)
99091294398832652748…53224638153103185919
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 2151804

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 c48f848ee13eae1ae51a011b1943cc6755ea26c3ff8ba1dbbc205b2d71f47c6a

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 #2,151,804 on Chainz β†—
Circulating Supply:57,860,970 XPMΒ·at block #6,827,097 Β· updates every 60s
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