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Home/Chain Registry/Block #2,272,880

Block #2,272,880

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2017, 4:55:20 AM Β· Difficulty 10.9544 Β· 4,570,245 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0e9662ea4a581f8f2d696cb8728151f964ad6f588d777d2ac74b19bd54ab853b
View on Chainz β†—

Difficulty

10.954421

Transactions

1

Size

200 B

Version

2

Bits

0af454e7

Nonce

68,116,598

Timestamp

8/29/2017, 4:55:20 AM

Confirmations

4,570,245

Merkle Root

3b6d1718d76b8e13a8b0b22faa6eaa661b4d68843ca9e9aadc50f5974b37d48f
Transactions (1)
Coinbase3b6d1718d76b8e…50f5974b37d48f
1 in β†’ 1 out8.3200 XPM110 B
AUZBGtR5…J9aj8ssS
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.

3.235 Γ— 10⁹³(94-digit number)
32351774307212825089…62880664994036664320
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
3.235 Γ— 10⁹³(94-digit number)
32351774307212825089…62880664994036664319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.235 Γ— 10⁹³(94-digit number)
32351774307212825089…62880664994036664321
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
6.470 Γ— 10⁹³(94-digit number)
64703548614425650179…25761329988073328639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.470 Γ— 10⁹³(94-digit number)
64703548614425650179…25761329988073328641
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
1.294 Γ— 10⁹⁴(95-digit number)
12940709722885130035…51522659976146657279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.294 Γ— 10⁹⁴(95-digit number)
12940709722885130035…51522659976146657281
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
2.588 Γ— 10⁹⁴(95-digit number)
25881419445770260071…03045319952293314559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.588 Γ— 10⁹⁴(95-digit number)
25881419445770260071…03045319952293314561
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
5.176 Γ— 10⁹⁴(95-digit number)
51762838891540520143…06090639904586629119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.176 Γ— 10⁹⁴(95-digit number)
51762838891540520143…06090639904586629121
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 2272880

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 0e9662ea4a581f8f2d696cb8728151f964ad6f588d777d2ac74b19bd54ab853b

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 #2,272,880 on Chainz β†—
Circulating Supply:57,989,366 XPMΒ·at block #6,843,124 Β· updates every 60s
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