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Block #549,495

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2014, 2:34:28 PM Β· Difficulty 10.9608 Β· 6,277,546 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00a0575575b8678c1ff7c3b1f7e23e05efe67582e25774ff6b2c606aacc10882
View on Chainz β†—

Height

#549,495

Difficulty

10.960822

Transactions

1

Size

208 B

Version

2

Bits

0af5f86b

Nonce

631,052,584

Timestamp

5/17/2014, 2:34:28 PM

Confirmations

6,277,546

Merkle Root

f1d7542c5be1e86c79bd79482a07713e60b19952b3fbefe3ab863a338040c542
Transactions (1)
Coinbasef1d7542c5be1e8…863a338040c542
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.701 Γ— 10⁹⁸(99-digit number)
37013111241780038345…35831538159176699360
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
3.701 Γ— 10⁹⁸(99-digit number)
37013111241780038345…35831538159176699359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.701 Γ— 10⁹⁸(99-digit number)
37013111241780038345…35831538159176699361
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
7.402 Γ— 10⁹⁸(99-digit number)
74026222483560076690…71663076318353398719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.402 Γ— 10⁹⁸(99-digit number)
74026222483560076690…71663076318353398721
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
1.480 Γ— 10⁹⁹(100-digit number)
14805244496712015338…43326152636706797439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.480 Γ— 10⁹⁹(100-digit number)
14805244496712015338…43326152636706797441
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
2.961 Γ— 10⁹⁹(100-digit number)
29610488993424030676…86652305273413594879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.961 Γ— 10⁹⁹(100-digit number)
29610488993424030676…86652305273413594881
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
5.922 Γ— 10⁹⁹(100-digit number)
59220977986848061352…73304610546827189759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.922 Γ— 10⁹⁹(100-digit number)
59220977986848061352…73304610546827189761
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 549495

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 00a0575575b8678c1ff7c3b1f7e23e05efe67582e25774ff6b2c606aacc10882

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 #549,495 on Chainz β†—
Circulating Supply:57,860,508 XPMΒ·at block #6,827,040 Β· updates every 60s
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