XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,613,038

Block #1,613,038

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2016, 12:30:35 AM Β· Difficulty 10.5998 Β· 5,214,142 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a1d8da3211d6e035216999076d7bbae8a2a9807fc1ce612e151da11f86216d82
View on Chainz β†—

Difficulty

10.599839

Transactions

1

Size

242 B

Version

2

Bits

0a998f0f

Nonce

784,581,744

Timestamp

6/4/2016, 12:30:35 AM

Confirmations

5,214,142

Merkle Root

3558d2f2d15ef75d6b9ead1bc0e6f57c0b0343ccb51c8283073eb2a5e6af97a2
Transactions (1)
Coinbase3558d2f2d15ef7…3eb2a5e6af97a2
1 in β†’ 2 out8.8900 XPM152 B
AK6BxZXL…UXnxyXDBALPu3s2c…EJXLjVFh
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.

6.638 Γ— 10⁹⁡(96-digit number)
66386490354792922907…04995424128245932920
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
6.638 Γ— 10⁹⁡(96-digit number)
66386490354792922907…04995424128245932919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.638 Γ— 10⁹⁡(96-digit number)
66386490354792922907…04995424128245932921
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
1.327 Γ— 10⁹⁢(97-digit number)
13277298070958584581…09990848256491865839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.327 Γ— 10⁹⁢(97-digit number)
13277298070958584581…09990848256491865841
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
2.655 Γ— 10⁹⁢(97-digit number)
26554596141917169162…19981696512983731679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.655 Γ— 10⁹⁢(97-digit number)
26554596141917169162…19981696512983731681
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
5.310 Γ— 10⁹⁢(97-digit number)
53109192283834338325…39963393025967463359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.310 Γ— 10⁹⁢(97-digit number)
53109192283834338325…39963393025967463361
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
1.062 Γ— 10⁹⁷(98-digit number)
10621838456766867665…79926786051934926719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10621838456766867665…79926786051934926721
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 1613038

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 a1d8da3211d6e035216999076d7bbae8a2a9807fc1ce612e151da11f86216d82

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 #1,613,038 on Chainz β†—
Circulating Supply:57,861,535 XPMΒ·at block #6,827,179 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