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Block #517,211

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2014, 7:33:34 PM Β· Difficulty 10.8508 Β· 6,326,060 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7c7f7f524db40b6275ea2c08963804ed3fb9fad392fd27240b3b0b7f74bdf709
View on Chainz β†—

Height

#517,211

Difficulty

10.850766

Transactions

1

Size

208 B

Version

2

Bits

0ad9cbcd

Nonce

238,097,189

Timestamp

4/29/2014, 7:33:34 PM

Confirmations

6,326,060

Merkle Root

99778c8ca075adb3d61a0f1828338ac7e377ca95ac95df96f9cbfa6b74a0ea1f
Transactions (1)
Coinbase99778c8ca075ad…cbfa6b74a0ea1f
1 in β†’ 1 out8.4800 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.

2.384 Γ— 10⁹⁹(100-digit number)
23849430562608885744…98072383597588601600
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
2.384 Γ— 10⁹⁹(100-digit number)
23849430562608885744…98072383597588601599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.384 Γ— 10⁹⁹(100-digit number)
23849430562608885744…98072383597588601601
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
4.769 Γ— 10⁹⁹(100-digit number)
47698861125217771488…96144767195177203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.769 Γ— 10⁹⁹(100-digit number)
47698861125217771488…96144767195177203201
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
9.539 Γ— 10⁹⁹(100-digit number)
95397722250435542977…92289534390354406399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.539 Γ— 10⁹⁹(100-digit number)
95397722250435542977…92289534390354406401
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
1.907 Γ— 10¹⁰⁰(101-digit number)
19079544450087108595…84579068780708812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.907 Γ— 10¹⁰⁰(101-digit number)
19079544450087108595…84579068780708812801
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
3.815 Γ— 10¹⁰⁰(101-digit number)
38159088900174217191…69158137561417625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.815 Γ— 10¹⁰⁰(101-digit number)
38159088900174217191…69158137561417625601
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 517211

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 7c7f7f524db40b6275ea2c08963804ed3fb9fad392fd27240b3b0b7f74bdf709

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 #517,211 on Chainz β†—
Circulating Supply:57,990,542 XPMΒ·at block #6,843,270 Β· updates every 60s
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