XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,635,277

Block #2,635,277

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 4:53:11 AM Β· Difficulty 11.3036 Β· 4,204,248 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4c4c2d3b79258744f681d1ef620f95bf341073dcd927fb6f79c0d0df596e243
View on Chainz β†—

Difficulty

11.303605

Transactions

1

Size

201 B

Version

2

Bits

0b4db913

Nonce

1,365,106,480

Timestamp

4/29/2018, 4:53:11 AM

Confirmations

4,204,248

Merkle Root

641336a05d187da21a65e873e90cc10a6ead3ac1a8304a3565c55b272c99e539
Transactions (1)
Coinbase641336a05d187d…c55b272c99e539
1 in β†’ 1 out7.8100 XPM110 B
ASrn44Ec…TtUa8daS
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.

1.217 Γ— 10⁹⁸(99-digit number)
12173188837626445659…82045799275884544000
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
1.217 Γ— 10⁹⁸(99-digit number)
12173188837626445659…82045799275884543999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.217 Γ— 10⁹⁸(99-digit number)
12173188837626445659…82045799275884544001
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
2.434 Γ— 10⁹⁸(99-digit number)
24346377675252891318…64091598551769087999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.434 Γ— 10⁹⁸(99-digit number)
24346377675252891318…64091598551769088001
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
4.869 Γ— 10⁹⁸(99-digit number)
48692755350505782636…28183197103538175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.869 Γ— 10⁹⁸(99-digit number)
48692755350505782636…28183197103538176001
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
9.738 Γ— 10⁹⁸(99-digit number)
97385510701011565272…56366394207076351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.738 Γ— 10⁹⁸(99-digit number)
97385510701011565272…56366394207076352001
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
1.947 Γ— 10⁹⁹(100-digit number)
19477102140202313054…12732788414152703999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.947 Γ— 10⁹⁹(100-digit number)
19477102140202313054…12732788414152704001
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
3.895 Γ— 10⁹⁹(100-digit number)
38954204280404626108…25465576828305407999
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 2635277

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 b4c4c2d3b79258744f681d1ef620f95bf341073dcd927fb6f79c0d0df596e243

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 #2,635,277 on Chainz β†—
Circulating Supply:57,960,500 XPMΒ·at block #6,839,524 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy