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Home/Chain Registry/Block #2,884,153

Block #2,884,153

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2018, 10:26:02 PM Β· Difficulty 11.6278 Β· 3,961,503 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d6386d79d8fe1e1d6c8893121938a624afb97c7c7f177a09b84090a18a4a29b9
View on Chainz β†—

Difficulty

11.627765

Transactions

1

Size

202 B

Version

2

Bits

0ba0b53c

Nonce

345,653,951

Timestamp

10/16/2018, 10:26:02 PM

Confirmations

3,961,503

Merkle Root

580204a070c3e35a723ec77c5edf0489541a0c70ca53c270bdbf613306db7146
Transactions (1)
Coinbase580204a070c3e3…bf613306db7146
1 in β†’ 1 out7.3800 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.237 Γ— 10⁹⁹(100-digit number)
12378139890788278309…58332397958540328960
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
1.237 Γ— 10⁹⁹(100-digit number)
12378139890788278309…58332397958540328959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.237 Γ— 10⁹⁹(100-digit number)
12378139890788278309…58332397958540328961
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
2.475 Γ— 10⁹⁹(100-digit number)
24756279781576556619…16664795917080657919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.475 Γ— 10⁹⁹(100-digit number)
24756279781576556619…16664795917080657921
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
4.951 Γ— 10⁹⁹(100-digit number)
49512559563153113238…33329591834161315839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.951 Γ— 10⁹⁹(100-digit number)
49512559563153113238…33329591834161315841
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
9.902 Γ— 10⁹⁹(100-digit number)
99025119126306226477…66659183668322631679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.902 Γ— 10⁹⁹(100-digit number)
99025119126306226477…66659183668322631681
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
1.980 Γ— 10¹⁰⁰(101-digit number)
19805023825261245295…33318367336645263359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.980 Γ— 10¹⁰⁰(101-digit number)
19805023825261245295…33318367336645263361
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
3.961 Γ— 10¹⁰⁰(101-digit number)
39610047650522490590…66636734673290526719
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 2884153

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 d6386d79d8fe1e1d6c8893121938a624afb97c7c7f177a09b84090a18a4a29b9

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 #2,884,153 on Chainz β†—
Circulating Supply:58,009,697 XPMΒ·at block #6,845,655 Β· updates every 60s
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