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Home/Chain Registry/Block #1,775,502

Block #1,775,502

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/23/2016, 3:29:23 AM Β· Difficulty 10.7585 Β· 5,038,654 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c2ab53aabca3fecd102c802e9207a9ddf558193cc0b4f986f7c8b9838e6364bb
View on Chainz β†—

Difficulty

10.758535

Transactions

1

Size

199 B

Version

2

Bits

0ac22f60

Nonce

569,564,470

Timestamp

9/23/2016, 3:29:23 AM

Confirmations

5,038,654

Merkle Root

3ed9bd72b3c9cb3880700dd3696b3b7c9a46d7367299427fbac69d77cce66acf
Transactions (1)
Coinbase3ed9bd72b3c9cb…c69d77cce66acf
1 in β†’ 1 out8.6300 XPM109 B
ASTd8Rg2…jPE9rnWK
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.

4.334 Γ— 10⁹⁴(95-digit number)
43343413711454360402…03476029625464247680
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
4.334 Γ— 10⁹⁴(95-digit number)
43343413711454360402…03476029625464247679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.334 Γ— 10⁹⁴(95-digit number)
43343413711454360402…03476029625464247681
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
8.668 Γ— 10⁹⁴(95-digit number)
86686827422908720804…06952059250928495359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.668 Γ— 10⁹⁴(95-digit number)
86686827422908720804…06952059250928495361
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
1.733 Γ— 10⁹⁡(96-digit number)
17337365484581744160…13904118501856990719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.733 Γ— 10⁹⁡(96-digit number)
17337365484581744160…13904118501856990721
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
3.467 Γ— 10⁹⁡(96-digit number)
34674730969163488321…27808237003713981439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.467 Γ— 10⁹⁡(96-digit number)
34674730969163488321…27808237003713981441
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
6.934 Γ— 10⁹⁡(96-digit number)
69349461938326976643…55616474007427962879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.934 Γ— 10⁹⁡(96-digit number)
69349461938326976643…55616474007427962881
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
1.386 Γ— 10⁹⁢(97-digit number)
13869892387665395328…11232948014855925759
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 1775502

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 c2ab53aabca3fecd102c802e9207a9ddf558193cc0b4f986f7c8b9838e6364bb

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 #1,775,502 on Chainz β†—
Circulating Supply:57,757,328 XPMΒ·at block #6,814,155 Β· updates every 60s
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