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Home/Chain Registry/Block #1,727,209

Block #1,727,209

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/21/2016, 8:03:08 AM Β· Difficulty 10.7011 Β· 5,112,663 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6cc931aa4c534dec044521c5b96f0f3b6508702b1dd2ca664818e734b2eafd29
View on Chainz β†—

Difficulty

10.701082

Transactions

2

Size

1.43 KB

Version

2

Bits

0ab37a1d

Nonce

264,779,559

Timestamp

8/21/2016, 8:03:08 AM

Confirmations

5,112,663

Merkle Root

ff7103a4f85c3634a285c4f09a0a51552ee37cc0b577dbdbf73a96cad3040576
Transactions (2)
Coinbase46d1556fced9bf…b521f7decf1367
1 in β†’ 1 out8.7400 XPM109 B
AagnEppD…9yePntDU
6984f0e69ab8c0…d05b46134a3891
8 in β†’ 2 out111.7163 XPM1.23 KB
AJdM6BQD…g1g59wtyAG9ysn6L…yD4toHES
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.

1.587 Γ— 10⁹⁸(99-digit number)
15872889672203475114…02958946625863352320
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
1.587 Γ— 10⁹⁸(99-digit number)
15872889672203475114…02958946625863352319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.587 Γ— 10⁹⁸(99-digit number)
15872889672203475114…02958946625863352321
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
3.174 Γ— 10⁹⁸(99-digit number)
31745779344406950229…05917893251726704639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.174 Γ— 10⁹⁸(99-digit number)
31745779344406950229…05917893251726704641
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
6.349 Γ— 10⁹⁸(99-digit number)
63491558688813900458…11835786503453409279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.349 Γ— 10⁹⁸(99-digit number)
63491558688813900458…11835786503453409281
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
1.269 Γ— 10⁹⁹(100-digit number)
12698311737762780091…23671573006906818559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.269 Γ— 10⁹⁹(100-digit number)
12698311737762780091…23671573006906818561
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
2.539 Γ— 10⁹⁹(100-digit number)
25396623475525560183…47343146013813637119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.539 Γ— 10⁹⁹(100-digit number)
25396623475525560183…47343146013813637121
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
5.079 Γ— 10⁹⁹(100-digit number)
50793246951051120366…94686292027627274239
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 1727209

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 6cc931aa4c534dec044521c5b96f0f3b6508702b1dd2ca664818e734b2eafd29

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 #1,727,209 on Chainz β†—
Circulating Supply:57,963,276 XPMΒ·at block #6,839,871 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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