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Home/Chain Registry/Block #2,470,691

Block #2,470,691

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2018, 7:21:03 AM Β· Difficulty 10.9611 Β· 4,371,497 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
85c17d51846fc9ca0bef4d2ab4596fb1ceb66e54bfecbd8e05b97fc5e8d2a3de
View on Chainz β†—

Difficulty

10.961132

Transactions

1

Size

201 B

Version

2

Bits

0af60cbc

Nonce

1,388,593,438

Timestamp

1/13/2018, 7:21:03 AM

Confirmations

4,371,497

Merkle Root

362c3ef15fa3f0c7c7eed362a7232f27d1e8eff36228953db1e045d1969e6c61
Transactions (1)
Coinbase362c3ef15fa3f0…e045d1969e6c61
1 in β†’ 1 out8.3100 XPM110 B
AaWPzo1L…fkksomSu
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.

1.612 Γ— 10⁹⁸(99-digit number)
16128895392635612037…35959106434489221120
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
1.612 Γ— 10⁹⁸(99-digit number)
16128895392635612037…35959106434489221119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.612 Γ— 10⁹⁸(99-digit number)
16128895392635612037…35959106434489221121
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
3.225 Γ— 10⁹⁸(99-digit number)
32257790785271224074…71918212868978442239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.225 Γ— 10⁹⁸(99-digit number)
32257790785271224074…71918212868978442241
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
6.451 Γ— 10⁹⁸(99-digit number)
64515581570542448149…43836425737956884479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.451 Γ— 10⁹⁸(99-digit number)
64515581570542448149…43836425737956884481
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
1.290 Γ— 10⁹⁹(100-digit number)
12903116314108489629…87672851475913768959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.290 Γ— 10⁹⁹(100-digit number)
12903116314108489629…87672851475913768961
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
2.580 Γ— 10⁹⁹(100-digit number)
25806232628216979259…75345702951827537919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.580 Γ— 10⁹⁹(100-digit number)
25806232628216979259…75345702951827537921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2470691

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 85c17d51846fc9ca0bef4d2ab4596fb1ceb66e54bfecbd8e05b97fc5e8d2a3de

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 #2,470,691 on Chainz β†—
Circulating Supply:57,981,897 XPMΒ·at block #6,842,187 Β· updates every 60s
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