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Home/Chain Registry/Block #2,122,664

Block #2,122,664

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/18/2017, 6:52:50 PM Β· Difficulty 10.9156 Β· 4,710,293 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ba892cd71719fe57de19a989ddf6f6d7ad01f32683f7fb6753877da7e4e6f35
View on Chainz β†—

Difficulty

10.915639

Transactions

1

Size

199 B

Version

2

Bits

0aea6756

Nonce

405,770,397

Timestamp

5/18/2017, 6:52:50 PM

Confirmations

4,710,293

Merkle Root

86ef5bcfd3527a1aa3a909e6adf063ec280b0032fa0238444c6a483035e34b1a
Transactions (1)
Coinbase86ef5bcfd3527a…6a483035e34b1a
1 in β†’ 1 out8.3800 XPM109 B
Abghq1Ys…r7tZm1vG
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.

2.889 Γ— 10⁹³(94-digit number)
28894647288962753020…51253590172336226660
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
2.889 Γ— 10⁹³(94-digit number)
28894647288962753020…51253590172336226659
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.889 Γ— 10⁹³(94-digit number)
28894647288962753020…51253590172336226661
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
5.778 Γ— 10⁹³(94-digit number)
57789294577925506040…02507180344672453319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.778 Γ— 10⁹³(94-digit number)
57789294577925506040…02507180344672453321
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
1.155 Γ— 10⁹⁴(95-digit number)
11557858915585101208…05014360689344906639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.155 Γ— 10⁹⁴(95-digit number)
11557858915585101208…05014360689344906641
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
2.311 Γ— 10⁹⁴(95-digit number)
23115717831170202416…10028721378689813279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.311 Γ— 10⁹⁴(95-digit number)
23115717831170202416…10028721378689813281
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
4.623 Γ— 10⁹⁴(95-digit number)
46231435662340404832…20057442757379626559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.623 Γ— 10⁹⁴(95-digit number)
46231435662340404832…20057442757379626561
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
9.246 Γ— 10⁹⁴(95-digit number)
92462871324680809664…40114885514759253119
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 2122664

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 0ba892cd71719fe57de19a989ddf6f6d7ad01f32683f7fb6753877da7e4e6f35

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 #2,122,664 on Chainz β†—
Circulating Supply:57,907,835 XPMΒ·at block #6,832,956 Β· updates every 60s
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