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Block #2,960,630

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/11/2018, 1:04:52 AM Β· Difficulty 11.3443 Β· 3,882,210 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
259f09e224a62e285d064705e4f5ded2f5eb4718455bcdd868658fdf88521bbf
View on Chainz β†—

Difficulty

11.344274

Transactions

1

Size

200 B

Version

2

Bits

0b582250

Nonce

284,893,629

Timestamp

12/11/2018, 1:04:52 AM

Confirmations

3,882,210

Merkle Root

e4c88d32655a7a99f9d514402df9fec4fbfa13994627dbd92f569cc03654cf27
Transactions (1)
Coinbasee4c88d32655a7a…569cc03654cf27
1 in β†’ 1 out7.7600 XPM109 B
AUMQRepm…tAfKmdW1
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.

1.143 Γ— 10⁹⁸(99-digit number)
11435067074890050985…50073300462293483520
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
1.143 Γ— 10⁹⁸(99-digit number)
11435067074890050985…50073300462293483519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.143 Γ— 10⁹⁸(99-digit number)
11435067074890050985…50073300462293483521
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
2.287 Γ— 10⁹⁸(99-digit number)
22870134149780101971…00146600924586967039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.287 Γ— 10⁹⁸(99-digit number)
22870134149780101971…00146600924586967041
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
4.574 Γ— 10⁹⁸(99-digit number)
45740268299560203943…00293201849173934079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.574 Γ— 10⁹⁸(99-digit number)
45740268299560203943…00293201849173934081
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
9.148 Γ— 10⁹⁸(99-digit number)
91480536599120407886…00586403698347868159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.148 Γ— 10⁹⁸(99-digit number)
91480536599120407886…00586403698347868161
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
1.829 Γ— 10⁹⁹(100-digit number)
18296107319824081577…01172807396695736319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.829 Γ— 10⁹⁹(100-digit number)
18296107319824081577…01172807396695736321
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
3.659 Γ— 10⁹⁹(100-digit number)
36592214639648163154…02345614793391472639
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 2960630

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 259f09e224a62e285d064705e4f5ded2f5eb4718455bcdd868658fdf88521bbf

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 #2,960,630 on Chainz β†—
Circulating Supply:57,987,064 XPMΒ·at block #6,842,839 Β· updates every 60s
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