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Block #849,030

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/11/2014, 1:02:31 PM Β· Difficulty 10.9713 Β· 5,995,510 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ec978f051ded6bbe771ba54f279a6b6fba5d060ab96346871cb636b95f3fd99
View on Chainz β†—

Height

#849,030

Difficulty

10.971308

Transactions

2

Size

432 B

Version

2

Bits

0af8a79d

Nonce

659,697,587

Timestamp

12/11/2014, 1:02:31 PM

Confirmations

5,995,510

Merkle Root

d2a8175d5d37b347d8689c8817bd3c1013443058d0847a0ac2b77ed917aa825d
Transactions (2)
Coinbase59984c3dc58358…b3118225bf06b3
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
505c67fb9daa2e…8247815d405e57
1 in β†’ 2 out0.1154 XPM226 B
AXUV4H7p…TDZgk7BEASVgf3vJ…FoRqNrvf
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.

3.402 Γ— 10⁹⁡(96-digit number)
34027756901864248627…03708144942086116960
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
3.402 Γ— 10⁹⁡(96-digit number)
34027756901864248627…03708144942086116959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.402 Γ— 10⁹⁡(96-digit number)
34027756901864248627…03708144942086116961
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
6.805 Γ— 10⁹⁡(96-digit number)
68055513803728497255…07416289884172233919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.805 Γ— 10⁹⁡(96-digit number)
68055513803728497255…07416289884172233921
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
1.361 Γ— 10⁹⁢(97-digit number)
13611102760745699451…14832579768344467839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.361 Γ— 10⁹⁢(97-digit number)
13611102760745699451…14832579768344467841
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
2.722 Γ— 10⁹⁢(97-digit number)
27222205521491398902…29665159536688935679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.722 Γ— 10⁹⁢(97-digit number)
27222205521491398902…29665159536688935681
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
5.444 Γ— 10⁹⁢(97-digit number)
54444411042982797804…59330319073377871359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.444 Γ— 10⁹⁢(97-digit number)
54444411042982797804…59330319073377871361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁷(98-digit number)
10888882208596559560…18660638146755742719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 849030

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 0ec978f051ded6bbe771ba54f279a6b6fba5d060ab96346871cb636b95f3fd99

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 #849,030 on Chainz β†—
Circulating Supply:58,000,723 XPMΒ·at block #6,844,539 Β· updates every 60s
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