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Home/Chain Registry/Block #2,244,108

Block #2,244,108

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2017, 4:29:15 PM Β· Difficulty 10.9470 Β· 4,597,877 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
463a9e1cb89d4aa8a524188e18adae9128e08a96610c2848990165fa963dea90
View on Chainz β†—

Difficulty

10.947043

Transactions

1

Size

201 B

Version

2

Bits

0af2716c

Nonce

377,354,995

Timestamp

8/9/2017, 4:29:15 PM

Confirmations

4,597,877

Merkle Root

7bb05a1420ec23f0a277ca9de5ac404217228caf526121ef89e81ab9acd3591f
Transactions (1)
Coinbase7bb05a1420ec23…e81ab9acd3591f
1 in β†’ 1 out8.3300 XPM110 B
AcDn9iaj…TqTFevYZ
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.

2.522 Γ— 10⁹⁢(97-digit number)
25222470140669575196…37686675315586780160
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
2.522 Γ— 10⁹⁢(97-digit number)
25222470140669575196…37686675315586780159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.522 Γ— 10⁹⁢(97-digit number)
25222470140669575196…37686675315586780161
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
5.044 Γ— 10⁹⁢(97-digit number)
50444940281339150392…75373350631173560319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.044 Γ— 10⁹⁢(97-digit number)
50444940281339150392…75373350631173560321
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
1.008 Γ— 10⁹⁷(98-digit number)
10088988056267830078…50746701262347120639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.008 Γ— 10⁹⁷(98-digit number)
10088988056267830078…50746701262347120641
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
2.017 Γ— 10⁹⁷(98-digit number)
20177976112535660156…01493402524694241279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.017 Γ— 10⁹⁷(98-digit number)
20177976112535660156…01493402524694241281
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
4.035 Γ— 10⁹⁷(98-digit number)
40355952225071320313…02986805049388482559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.035 Γ— 10⁹⁷(98-digit number)
40355952225071320313…02986805049388482561
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
8.071 Γ— 10⁹⁷(98-digit number)
80711904450142640627…05973610098776965119
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 2244108

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 463a9e1cb89d4aa8a524188e18adae9128e08a96610c2848990165fa963dea90

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 #2,244,108 on Chainz β†—
Circulating Supply:57,980,266 XPMΒ·at block #6,841,984 Β· updates every 60s
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