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Block #363,949

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/17/2014, 6:13:55 PM Β· Difficulty 10.4176 Β· 6,468,156 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
db1df00f3761a164cf718fb868f5da0a7632ce335fadcd4ed992a322d92d7b14
View on Chainz β†—

Height

#363,949

Difficulty

10.417612

Transactions

1

Size

207 B

Version

2

Bits

0a6ae899

Nonce

415,381

Timestamp

1/17/2014, 6:13:55 PM

Confirmations

6,468,156

Merkle Root

9204891307645f048b1a4716b4cbaf0a48bbd143e51c7ee0b8313cab24872166
Transactions (1)
Coinbase9204891307645f…313cab24872166
1 in β†’ 1 out9.2000 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.

1.572 Γ— 10⁹⁸(99-digit number)
15729846724899019458…07047835173193798400
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
1.572 Γ— 10⁹⁸(99-digit number)
15729846724899019458…07047835173193798399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.572 Γ— 10⁹⁸(99-digit number)
15729846724899019458…07047835173193798401
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
3.145 Γ— 10⁹⁸(99-digit number)
31459693449798038917…14095670346387596799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.145 Γ— 10⁹⁸(99-digit number)
31459693449798038917…14095670346387596801
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
6.291 Γ— 10⁹⁸(99-digit number)
62919386899596077834…28191340692775193599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.291 Γ— 10⁹⁸(99-digit number)
62919386899596077834…28191340692775193601
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
1.258 Γ— 10⁹⁹(100-digit number)
12583877379919215566…56382681385550387199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.258 Γ— 10⁹⁹(100-digit number)
12583877379919215566…56382681385550387201
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
2.516 Γ— 10⁹⁹(100-digit number)
25167754759838431133…12765362771100774399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.516 Γ— 10⁹⁹(100-digit number)
25167754759838431133…12765362771100774401
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 363949

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 db1df00f3761a164cf718fb868f5da0a7632ce335fadcd4ed992a322d92d7b14

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 #363,949 on Chainz β†—
Circulating Supply:57,900,970 XPMΒ·at block #6,832,104 Β· updates every 60s
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