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Block #549,799

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2014, 7:01:59 PM Β· Difficulty 10.9611 Β· 6,265,007 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ad64ff5d7c6bcb266a95ec8fd7d5d1a59fb28f8bfe82ba630f312deef6460556
View on Chainz β†—

Height

#549,799

Difficulty

10.961138

Transactions

1

Size

201 B

Version

2

Bits

0af60d21

Nonce

49,936,207

Timestamp

5/17/2014, 7:01:59 PM

Confirmations

6,265,007

Merkle Root

1de5246d1b504496fa4e30587e06b455efc8c8c0be9f08f009f7771e10505d0c
Transactions (1)
Coinbase1de5246d1b5044…f7771e10505d0c
1 in β†’ 1 out8.3100 XPM109 B
ALovyv92…pAU61MhS
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.

2.774 Γ— 10⁹⁸(99-digit number)
27740813936231674537…43658752328242769920
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
2.774 Γ— 10⁹⁸(99-digit number)
27740813936231674537…43658752328242769919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.774 Γ— 10⁹⁸(99-digit number)
27740813936231674537…43658752328242769921
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
5.548 Γ— 10⁹⁸(99-digit number)
55481627872463349074…87317504656485539839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.548 Γ— 10⁹⁸(99-digit number)
55481627872463349074…87317504656485539841
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
1.109 Γ— 10⁹⁹(100-digit number)
11096325574492669814…74635009312971079679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.109 Γ— 10⁹⁹(100-digit number)
11096325574492669814…74635009312971079681
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
2.219 Γ— 10⁹⁹(100-digit number)
22192651148985339629…49270018625942159359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.219 Γ— 10⁹⁹(100-digit number)
22192651148985339629…49270018625942159361
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
4.438 Γ— 10⁹⁹(100-digit number)
44385302297970679259…98540037251884318719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.438 Γ— 10⁹⁹(100-digit number)
44385302297970679259…98540037251884318721
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
8.877 Γ— 10⁹⁹(100-digit number)
88770604595941358518…97080074503768637439
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 549799

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 ad64ff5d7c6bcb266a95ec8fd7d5d1a59fb28f8bfe82ba630f312deef6460556

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 #549,799 on Chainz β†—
Circulating Supply:57,762,534 XPMΒ·at block #6,814,805 Β· updates every 60s
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