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Block #839,728

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2014, 3:08:25 PM Β· Difficulty 10.9745 Β· 6,004,792 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ade0157f53a7dde392e45122853762c87cbaa794d0e785a1e7e21bdd81a82c9b
View on Chainz β†—

Height

#839,728

Difficulty

10.974529

Transactions

2

Size

434 B

Version

2

Bits

0af97ab7

Nonce

162,563,625

Timestamp

12/4/2014, 3:08:25 PM

Confirmations

6,004,792

Merkle Root

7235f3de391190a8420484bb5acc9a4ca1246dee1eab542e99a2cf1b89c9af78
Transactions (2)
Coinbase9d5743e89311aa…e637222c16b431
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
e403211f5dccd7…87b089b5bf438f
1 in β†’ 2 out0.3558 XPM227 B
AWtEqtfs…KxQ32PxLAQgFdsdP…6PfumxWS
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.

2.208 Γ— 10⁹⁢(97-digit number)
22089079702797681782…72489510856158221360
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
2.208 Γ— 10⁹⁢(97-digit number)
22089079702797681782…72489510856158221359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.208 Γ— 10⁹⁢(97-digit number)
22089079702797681782…72489510856158221361
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
4.417 Γ— 10⁹⁢(97-digit number)
44178159405595363564…44979021712316442719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.417 Γ— 10⁹⁢(97-digit number)
44178159405595363564…44979021712316442721
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
8.835 Γ— 10⁹⁢(97-digit number)
88356318811190727128…89958043424632885439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.835 Γ— 10⁹⁢(97-digit number)
88356318811190727128…89958043424632885441
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
1.767 Γ— 10⁹⁷(98-digit number)
17671263762238145425…79916086849265770879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.767 Γ— 10⁹⁷(98-digit number)
17671263762238145425…79916086849265770881
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
3.534 Γ— 10⁹⁷(98-digit number)
35342527524476290851…59832173698531541759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.534 Γ— 10⁹⁷(98-digit number)
35342527524476290851…59832173698531541761
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 839728

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 ade0157f53a7dde392e45122853762c87cbaa794d0e785a1e7e21bdd81a82c9b

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 #839,728 on Chainz β†—
Circulating Supply:58,000,559 XPMΒ·at block #6,844,519 Β· updates every 60s
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