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Home/Chain Registry/Block #2,202,168

Block #2,202,168

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2017, 8:00:22 AM Β· Difficulty 10.9492 Β· 4,643,172 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00f2e1f624cdd57ce3a8124f57d0f0f1bfb5dc19c221ba5765b59c31edd35623
View on Chainz β†—

Difficulty

10.949195

Transactions

1

Size

200 B

Version

2

Bits

0af2fe6f

Nonce

1,366,217,491

Timestamp

7/11/2017, 8:00:22 AM

Confirmations

4,643,172

Merkle Root

aded980359fe5316340ed009752c9d2cda821d96f920ae12e5be04170256534b
Transactions (1)
Coinbaseaded980359fe53…be04170256534b
1 in β†’ 1 out8.3300 XPM110 B
AW2e6Hbc…9o5k5sDN
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.

5.430 Γ— 10⁹³(94-digit number)
54306521106543006222…59794026234040451250
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
5.430 Γ— 10⁹³(94-digit number)
54306521106543006222…59794026234040451249
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.430 Γ— 10⁹³(94-digit number)
54306521106543006222…59794026234040451251
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
1.086 Γ— 10⁹⁴(95-digit number)
10861304221308601244…19588052468080902499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.086 Γ— 10⁹⁴(95-digit number)
10861304221308601244…19588052468080902501
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
2.172 Γ— 10⁹⁴(95-digit number)
21722608442617202489…39176104936161804999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.172 Γ— 10⁹⁴(95-digit number)
21722608442617202489…39176104936161805001
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
4.344 Γ— 10⁹⁴(95-digit number)
43445216885234404978…78352209872323609999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.344 Γ— 10⁹⁴(95-digit number)
43445216885234404978…78352209872323610001
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
8.689 Γ— 10⁹⁴(95-digit number)
86890433770468809956…56704419744647219999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.689 Γ— 10⁹⁴(95-digit number)
86890433770468809956…56704419744647220001
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 2202168

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 00f2e1f624cdd57ce3a8124f57d0f0f1bfb5dc19c221ba5765b59c31edd35623

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 #2,202,168 on Chainz β†—
Circulating Supply:58,007,162 XPMΒ·at block #6,845,339 Β· updates every 60s
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