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Home/Chain Registry/Block #1,609,837

Block #1,609,837

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2016, 4:34:09 PM Β· Difficulty 10.6121 Β· 5,232,455 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
005396adef0e3d623a9d2dbfc34edd7b3477a33862779607919466958d5e3adc
View on Chainz β†—

Difficulty

10.612054

Transactions

1

Size

200 B

Version

2

Bits

0a9caf98

Nonce

1,469,408,174

Timestamp

6/1/2016, 4:34:09 PM

Confirmations

5,232,455

Merkle Root

01f0390d13f20eba8efbe7f65ad84b18c28dabde74284335001fb7ee89ad1520
Transactions (1)
Coinbase01f0390d13f20e…1fb7ee89ad1520
1 in β†’ 1 out8.8700 XPM110 B
AN3XTwc5…soXfnFeR
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.

5.286 Γ— 10⁹³(94-digit number)
52862335593988820766…10450250722908052320
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
5.286 Γ— 10⁹³(94-digit number)
52862335593988820766…10450250722908052319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.286 Γ— 10⁹³(94-digit number)
52862335593988820766…10450250722908052321
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
1.057 Γ— 10⁹⁴(95-digit number)
10572467118797764153…20900501445816104639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.057 Γ— 10⁹⁴(95-digit number)
10572467118797764153…20900501445816104641
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
2.114 Γ— 10⁹⁴(95-digit number)
21144934237595528306…41801002891632209279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.114 Γ— 10⁹⁴(95-digit number)
21144934237595528306…41801002891632209281
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
4.228 Γ— 10⁹⁴(95-digit number)
42289868475191056612…83602005783264418559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.228 Γ— 10⁹⁴(95-digit number)
42289868475191056612…83602005783264418561
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
8.457 Γ— 10⁹⁴(95-digit number)
84579736950382113225…67204011566528837119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.457 Γ— 10⁹⁴(95-digit number)
84579736950382113225…67204011566528837121
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 1609837

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 005396adef0e3d623a9d2dbfc34edd7b3477a33862779607919466958d5e3adc

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 #1,609,837 on Chainz β†—
Circulating Supply:57,982,740 XPMΒ·at block #6,842,291 Β· updates every 60s
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