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Block #419,707

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/25/2014, 9:19:23 PM Β· Difficulty 10.3682 Β· 6,406,531 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
781d9f50e59f4005a0bffcc4a00b33493c32b04e96e785398b51bb3367985f81
View on Chainz β†—

Height

#419,707

Difficulty

10.368161

Transactions

1

Size

206 B

Version

2

Bits

0a5e3fd1

Nonce

120,278

Timestamp

2/25/2014, 9:19:23 PM

Confirmations

6,406,531

Merkle Root

cbf3d0dc830dcd56f39ce8b2eed525529a89a22821ae9aa8c3545cceaa92aa81
Transactions (1)
Coinbasecbf3d0dc830dcd…545cceaa92aa81
1 in β†’ 1 out9.2900 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.

2.753 Γ— 10⁹⁡(96-digit number)
27537789491069630815…43379315796419543040
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
2.753 Γ— 10⁹⁡(96-digit number)
27537789491069630815…43379315796419543039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.753 Γ— 10⁹⁡(96-digit number)
27537789491069630815…43379315796419543041
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
5.507 Γ— 10⁹⁡(96-digit number)
55075578982139261630…86758631592839086079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.507 Γ— 10⁹⁡(96-digit number)
55075578982139261630…86758631592839086081
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
1.101 Γ— 10⁹⁢(97-digit number)
11015115796427852326…73517263185678172159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.101 Γ— 10⁹⁢(97-digit number)
11015115796427852326…73517263185678172161
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
2.203 Γ— 10⁹⁢(97-digit number)
22030231592855704652…47034526371356344319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.203 Γ— 10⁹⁢(97-digit number)
22030231592855704652…47034526371356344321
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
4.406 Γ— 10⁹⁢(97-digit number)
44060463185711409304…94069052742712688639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.406 Γ— 10⁹⁢(97-digit number)
44060463185711409304…94069052742712688641
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 419707

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 781d9f50e59f4005a0bffcc4a00b33493c32b04e96e785398b51bb3367985f81

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 #419,707 on Chainz β†—
Circulating Supply:57,854,036 XPMΒ·at block #6,826,237 Β· updates every 60s
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