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Home/Chain Registry/Block #2,621,648

Block #2,621,648

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/20/2018, 2:18:28 AM Β· Difficulty 11.2283 Β· 4,209,704 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c32a01e4d93584274d9c84d42f4ce87cf5772adfa530205c4fc546bf68f1dcd
View on Chainz β†—

Difficulty

11.228288

Transactions

1

Size

202 B

Version

2

Bits

0b3a7116

Nonce

2,043,136,962

Timestamp

4/20/2018, 2:18:28 AM

Confirmations

4,209,704

Merkle Root

5c5bbf4761689d8150c8976f4d5686794b0a3350bb55cd8d1feb4535d2f4de6c
Transactions (1)
Coinbase5c5bbf4761689d…eb4535d2f4de6c
1 in β†’ 1 out7.9200 XPM110 B
AGQUxfH5…k2RpB46J
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.

1.034 Γ— 10⁹⁹(100-digit number)
10347085827417880107…75007036377532989440
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
1.034 Γ— 10⁹⁹(100-digit number)
10347085827417880107…75007036377532989439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.034 Γ— 10⁹⁹(100-digit number)
10347085827417880107…75007036377532989441
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
2.069 Γ— 10⁹⁹(100-digit number)
20694171654835760214…50014072755065978879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.069 Γ— 10⁹⁹(100-digit number)
20694171654835760214…50014072755065978881
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
4.138 Γ— 10⁹⁹(100-digit number)
41388343309671520428…00028145510131957759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.138 Γ— 10⁹⁹(100-digit number)
41388343309671520428…00028145510131957761
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
8.277 Γ— 10⁹⁹(100-digit number)
82776686619343040856…00056291020263915519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.277 Γ— 10⁹⁹(100-digit number)
82776686619343040856…00056291020263915521
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
1.655 Γ— 10¹⁰⁰(101-digit number)
16555337323868608171…00112582040527831039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.655 Γ— 10¹⁰⁰(101-digit number)
16555337323868608171…00112582040527831041
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
3.311 Γ— 10¹⁰⁰(101-digit number)
33110674647737216342…00225164081055662079
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 2621648

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 6c32a01e4d93584274d9c84d42f4ce87cf5772adfa530205c4fc546bf68f1dcd

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 #2,621,648 on Chainz β†—
Circulating Supply:57,894,969 XPMΒ·at block #6,831,351 Β· updates every 60s
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