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Block #513,416

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/27/2014, 12:34:38 PM Β· Difficulty 10.8351 Β· 6,318,247 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
445d969a106694120aa2cb4cf8b5085c0ad8d5e11ecafb4716c5add0c4891c99
View on Chainz β†—

Height

#513,416

Difficulty

10.835091

Transactions

1

Size

208 B

Version

2

Bits

0ad5c88d

Nonce

98,554,691

Timestamp

4/27/2014, 12:34:38 PM

Confirmations

6,318,247

Merkle Root

36d57badd7c483a87329690a4b1554db123b76ad7d52f85cea3f2f9f3e3d2eb1
Transactions (1)
Coinbase36d57badd7c483…3f2f9f3e3d2eb1
1 in β†’ 1 out8.5000 XPM116 B
AbwWkWZt…kawDhufa
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.

2.278 Γ— 10⁹⁸(99-digit number)
22784610293728108646…24379609090842804960
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
2.278 Γ— 10⁹⁸(99-digit number)
22784610293728108646…24379609090842804959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.278 Γ— 10⁹⁸(99-digit number)
22784610293728108646…24379609090842804961
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
4.556 Γ— 10⁹⁸(99-digit number)
45569220587456217292…48759218181685609919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.556 Γ— 10⁹⁸(99-digit number)
45569220587456217292…48759218181685609921
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
9.113 Γ— 10⁹⁸(99-digit number)
91138441174912434585…97518436363371219839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.113 Γ— 10⁹⁸(99-digit number)
91138441174912434585…97518436363371219841
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
1.822 Γ— 10⁹⁹(100-digit number)
18227688234982486917…95036872726742439679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.822 Γ— 10⁹⁹(100-digit number)
18227688234982486917…95036872726742439681
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
3.645 Γ— 10⁹⁹(100-digit number)
36455376469964973834…90073745453484879359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.645 Γ— 10⁹⁹(100-digit number)
36455376469964973834…90073745453484879361
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 513416

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 445d969a106694120aa2cb4cf8b5085c0ad8d5e11ecafb4716c5add0c4891c99

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 #513,416 on Chainz β†—
Circulating Supply:57,897,411 XPMΒ·at block #6,831,662 Β· updates every 60s
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