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Block #839,626

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2014, 1:27:14 PM Β· Difficulty 10.9745 Β· 6,005,755 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d6866d3528bb3a8f3bf55b1a753d34508366b410b1bccefd2ddde1bc0672d50
View on Chainz β†—

Height

#839,626

Difficulty

10.974524

Transactions

2

Size

433 B

Version

2

Bits

0af97a6b

Nonce

2,230,627,720

Timestamp

12/4/2014, 1:27:14 PM

Confirmations

6,005,755

Merkle Root

169ae226a6732767616c0277ad9d0ee151c4ab32dd2f64869d21c7f8527643e2
Transactions (2)
Coinbased40bbf21825668…445bd0def13608
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
4f46a42160b1b8…a958db5056b693
1 in β†’ 2 out0.4963 XPM226 B
AXMbc3ss…STSXahgVAYqqg3mE…njC7CaAq
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.

8.363 Γ— 10⁹⁡(96-digit number)
83637507036481621649…45811621354763079680
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
8.363 Γ— 10⁹⁡(96-digit number)
83637507036481621649…45811621354763079679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.363 Γ— 10⁹⁡(96-digit number)
83637507036481621649…45811621354763079681
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
1.672 Γ— 10⁹⁢(97-digit number)
16727501407296324329…91623242709526159359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.672 Γ— 10⁹⁢(97-digit number)
16727501407296324329…91623242709526159361
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
3.345 Γ— 10⁹⁢(97-digit number)
33455002814592648659…83246485419052318719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.345 Γ— 10⁹⁢(97-digit number)
33455002814592648659…83246485419052318721
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
6.691 Γ— 10⁹⁢(97-digit number)
66910005629185297319…66492970838104637439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.691 Γ— 10⁹⁢(97-digit number)
66910005629185297319…66492970838104637441
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
1.338 Γ— 10⁹⁷(98-digit number)
13382001125837059463…32985941676209274879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13382001125837059463…32985941676209274881
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
2.676 Γ— 10⁹⁷(98-digit number)
26764002251674118927…65971883352418549759
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 839626

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 3d6866d3528bb3a8f3bf55b1a753d34508366b410b1bccefd2ddde1bc0672d50

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 #839,626 on Chainz β†—
Circulating Supply:58,007,493 XPMΒ·at block #6,845,380 Β· updates every 60s
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