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Home/Chain Registry/Block #2,653,758

Block #2,653,758

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2018, 4:38:33 PM Β· Difficulty 11.7327 Β· 4,177,118 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0a1116a3c69618dd6acc7c5501f27779ec59e54fb791522ff8e2f9a4334c0675
View on Chainz β†—

Difficulty

11.732672

Transactions

2

Size

425 B

Version

2

Bits

0bbb9060

Nonce

347,889,814

Timestamp

5/8/2018, 4:38:33 PM

Confirmations

4,177,118

Merkle Root

a90aa62811de21b77a3f93169ce3b7e245aed48d92b97abecd47e2f51fe2a4b1
Transactions (2)
Coinbase3d5c02f4345fb1…3d2cff8ee7e73f
1 in β†’ 1 out7.2600 XPM109 B
Adqah8zh…1WwoHJ9t
3bfc075db4b160…5e4f0de33e668f
1 in β†’ 2 out1.0338 XPM227 B
AUrqu5L2…ZkgSBdjQAHmoHaoV…guxDRZ3w
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.

1.226 Γ— 10⁹²(93-digit number)
12265649248717645883…89506199505033953200
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
1.226 Γ— 10⁹²(93-digit number)
12265649248717645883…89506199505033953199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.226 Γ— 10⁹²(93-digit number)
12265649248717645883…89506199505033953201
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
2.453 Γ— 10⁹²(93-digit number)
24531298497435291766…79012399010067906399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.453 Γ— 10⁹²(93-digit number)
24531298497435291766…79012399010067906401
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
4.906 Γ— 10⁹²(93-digit number)
49062596994870583533…58024798020135812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.906 Γ— 10⁹²(93-digit number)
49062596994870583533…58024798020135812801
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
9.812 Γ— 10⁹²(93-digit number)
98125193989741167067…16049596040271625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.812 Γ— 10⁹²(93-digit number)
98125193989741167067…16049596040271625601
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
1.962 Γ— 10⁹³(94-digit number)
19625038797948233413…32099192080543251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.962 Γ— 10⁹³(94-digit number)
19625038797948233413…32099192080543251201
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
3.925 Γ— 10⁹³(94-digit number)
39250077595896466826…64198384161086502399
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 2653758

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 0a1116a3c69618dd6acc7c5501f27779ec59e54fb791522ff8e2f9a4334c0675

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 #2,653,758 on Chainz β†—
Circulating Supply:57,891,146 XPMΒ·at block #6,830,875 Β· updates every 60s
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