XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,506,164

Block #3,506,164

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2020, 3:27:32 AM Β· Difficulty 10.9304 Β· 3,320,127 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e80d466d99d6798449676e300add78ff685c96fa7e3eadaad47109deea713988
View on Chainz β†—

Difficulty

10.930371

Transactions

1

Size

200 B

Version

2

Bits

0aee2cc3

Nonce

471,651,416

Timestamp

1/9/2020, 3:27:32 AM

Confirmations

3,320,127

Merkle Root

18df586e8d66f0830d035f22d998952e14b2013c5a08b544d334c398d868176d
Transactions (1)
Coinbase18df586e8d66f0…34c398d868176d
1 in β†’ 1 out8.3600 XPM109 B
AXfJqzUb…HXeXmjMz
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.

9.984 Γ— 10⁹⁡(96-digit number)
99844431084779803640…26737956936222608640
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
9.984 Γ— 10⁹⁡(96-digit number)
99844431084779803640…26737956936222608639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.984 Γ— 10⁹⁡(96-digit number)
99844431084779803640…26737956936222608641
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
1.996 Γ— 10⁹⁢(97-digit number)
19968886216955960728…53475913872445217279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.996 Γ— 10⁹⁢(97-digit number)
19968886216955960728…53475913872445217281
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
3.993 Γ— 10⁹⁢(97-digit number)
39937772433911921456…06951827744890434559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.993 Γ— 10⁹⁢(97-digit number)
39937772433911921456…06951827744890434561
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
7.987 Γ— 10⁹⁢(97-digit number)
79875544867823842912…13903655489780869119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.987 Γ— 10⁹⁢(97-digit number)
79875544867823842912…13903655489780869121
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
1.597 Γ— 10⁹⁷(98-digit number)
15975108973564768582…27807310979561738239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.597 Γ— 10⁹⁷(98-digit number)
15975108973564768582…27807310979561738241
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
3.195 Γ— 10⁹⁷(98-digit number)
31950217947129537165…55614621959123476479
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 3506164

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 e80d466d99d6798449676e300add78ff685c96fa7e3eadaad47109deea713988

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 #3,506,164 on Chainz β†—
Circulating Supply:57,854,467 XPMΒ·at block #6,826,290 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