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Home/Chain Registry/Block #2,878,848

Block #2,878,848

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 10/13/2018, 2:20:57 AM Β· Difficulty 11.6433 Β· 3,961,237 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0573989bfe9603ee83e033502b601e768765e4e6ca2ee2b9e9f23326111785d1
View on Chainz β†—

Difficulty

11.643340

Transactions

1

Size

200 B

Version

2

Bits

0ba4b1f4

Nonce

45,320,271

Timestamp

10/13/2018, 2:20:57 AM

Confirmations

3,961,237

Merkle Root

41d7923aabe7ab97b0cc25cd58de768659c222e011d69b4c010bf1bfc7db0858
Transactions (1)
Coinbase41d7923aabe7ab…0bf1bfc7db0858
1 in β†’ 1 out7.3600 XPM110 B
APHtoGQy…ep6QfKrN
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.

2.650 Γ— 10⁹⁡(96-digit number)
26500436571513418290…92468882095972865280
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
2.650 Γ— 10⁹⁡(96-digit number)
26500436571513418290…92468882095972865279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.650 Γ— 10⁹⁡(96-digit number)
26500436571513418290…92468882095972865281
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
5.300 Γ— 10⁹⁡(96-digit number)
53000873143026836581…84937764191945730559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.300 Γ— 10⁹⁡(96-digit number)
53000873143026836581…84937764191945730561
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
1.060 Γ— 10⁹⁢(97-digit number)
10600174628605367316…69875528383891461119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.060 Γ— 10⁹⁢(97-digit number)
10600174628605367316…69875528383891461121
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
2.120 Γ— 10⁹⁢(97-digit number)
21200349257210734632…39751056767782922239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.120 Γ— 10⁹⁢(97-digit number)
21200349257210734632…39751056767782922241
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
4.240 Γ— 10⁹⁢(97-digit number)
42400698514421469265…79502113535565844479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.240 Γ— 10⁹⁢(97-digit number)
42400698514421469265…79502113535565844481
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
8.480 Γ— 10⁹⁢(97-digit number)
84801397028842938530…59004227071131688959
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.480 Γ— 10⁹⁢(97-digit number)
84801397028842938530…59004227071131688961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2878848

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 0573989bfe9603ee83e033502b601e768765e4e6ca2ee2b9e9f23326111785d1

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 #2,878,848 on Chainz β†—
Circulating Supply:57,964,989 XPMΒ·at block #6,840,084 Β· updates every 60s
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