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Home/Chain Registry/Block #2,669,611

Block #2,669,611

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/20/2018, 8:10:21 AM Β· Difficulty 11.6797 Β· 4,167,062 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
200e1ef204e3b6e93221ac3bbf687492e6429debce62e7248cc3dbe9613c7bea
View on Chainz β†—

Difficulty

11.679735

Transactions

2

Size

572 B

Version

2

Bits

0bae0323

Nonce

2,635,107

Timestamp

5/20/2018, 8:10:21 AM

Confirmations

4,167,062

Merkle Root

c05d747cec63fb741b46efbea92f3aae711100cd9f66d7617624813b29a0c3d3
Transactions (2)
Coinbase7f184e48bb0f49…a61337cabd0bd3
1 in β†’ 1 out7.3300 XPM110 B
AbV2sRfC…apBmdCy6
a1c887cd879ffe…ea2c30cd4e332c
2 in β†’ 2 out140.9376 XPM372 B
AVztRMH9…VSbKNtnsAMacMFhM…iFNVuut4
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.

2.245 Γ— 10⁹⁴(95-digit number)
22456811230634798923…49422552151369410960
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
2.245 Γ— 10⁹⁴(95-digit number)
22456811230634798923…49422552151369410959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.245 Γ— 10⁹⁴(95-digit number)
22456811230634798923…49422552151369410961
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
4.491 Γ— 10⁹⁴(95-digit number)
44913622461269597847…98845104302738821919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.491 Γ— 10⁹⁴(95-digit number)
44913622461269597847…98845104302738821921
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
8.982 Γ— 10⁹⁴(95-digit number)
89827244922539195695…97690208605477643839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.982 Γ— 10⁹⁴(95-digit number)
89827244922539195695…97690208605477643841
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
1.796 Γ— 10⁹⁡(96-digit number)
17965448984507839139…95380417210955287679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.796 Γ— 10⁹⁡(96-digit number)
17965448984507839139…95380417210955287681
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
3.593 Γ— 10⁹⁡(96-digit number)
35930897969015678278…90760834421910575359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.593 Γ— 10⁹⁡(96-digit number)
35930897969015678278…90760834421910575361
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
7.186 Γ— 10⁹⁡(96-digit number)
71861795938031356556…81521668843821150719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
7.186 Γ— 10⁹⁡(96-digit number)
71861795938031356556…81521668843821150721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2669611

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 200e1ef204e3b6e93221ac3bbf687492e6429debce62e7248cc3dbe9613c7bea

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 #2,669,611 on Chainz β†—
Circulating Supply:57,937,663 XPMΒ·at block #6,836,672 Β· updates every 60s
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