XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,701,583

Block #2,701,583

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/12/2018, 1:39:29 AM Β· Difficulty 11.6291 Β· 4,131,458 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9cfa5aa5377b903549b178d440a148e4fc9c0c613d28c06119e45ad4c20f16f7
View on Chainz β†—

Difficulty

11.629058

Transactions

1

Size

201 B

Version

2

Bits

0ba109f0

Nonce

978,177,748

Timestamp

6/12/2018, 1:39:29 AM

Confirmations

4,131,458

Merkle Root

3d8ed62929c9417badafd4f0bd5705a08745c45af97b5b8cb6b9a6395b990673
Transactions (1)
Coinbase3d8ed62929c941…b9a6395b990673
1 in β†’ 1 out7.3800 XPM110 B
AXh6z9Hq…vpUbEduB
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.

2.782 Γ— 10⁹⁷(98-digit number)
27828277425614464643…57148890392550604800
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
2.782 Γ— 10⁹⁷(98-digit number)
27828277425614464643…57148890392550604799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.782 Γ— 10⁹⁷(98-digit number)
27828277425614464643…57148890392550604801
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
5.565 Γ— 10⁹⁷(98-digit number)
55656554851228929287…14297780785101209599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.565 Γ— 10⁹⁷(98-digit number)
55656554851228929287…14297780785101209601
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
1.113 Γ— 10⁹⁸(99-digit number)
11131310970245785857…28595561570202419199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.113 Γ— 10⁹⁸(99-digit number)
11131310970245785857…28595561570202419201
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
2.226 Γ— 10⁹⁸(99-digit number)
22262621940491571714…57191123140404838399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.226 Γ— 10⁹⁸(99-digit number)
22262621940491571714…57191123140404838401
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
4.452 Γ— 10⁹⁸(99-digit number)
44525243880983143429…14382246280809676799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.452 Γ— 10⁹⁸(99-digit number)
44525243880983143429…14382246280809676801
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
8.905 Γ— 10⁹⁸(99-digit number)
89050487761966286859…28764492561619353599
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 2701583

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 9cfa5aa5377b903549b178d440a148e4fc9c0c613d28c06119e45ad4c20f16f7

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 #2,701,583 on Chainz β†—
Circulating Supply:57,908,506 XPMΒ·at block #6,833,040 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