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Home/Chain Registry/Block #2,772,961

Block #2,772,961

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2018, 7:59:36 AM Β· Difficulty 11.6623 Β· 4,064,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
714f53ab4603174d844617ae7de4b46f60b9c9dd012ab427439182c95ef10418
View on Chainz β†—

Difficulty

11.662347

Transactions

2

Size

1018 B

Version

2

Bits

0ba98f99

Nonce

86,330,939

Timestamp

7/31/2018, 7:59:36 AM

Confirmations

4,064,111

Merkle Root

8a7d9af8172159f53e317e926dbd2ea415124202d88affb87df7cf2865fcdf35
Transactions (2)
Coinbase8d88d84a2c7045…ae268df93fb67d
1 in β†’ 1 out7.3500 XPM110 B
AYYeiZ21…H9i7sts2
3afd14ad6463a9…e4fca35f10c33a
5 in β†’ 2 out210.8267 XPM819 B
AN7L9gAS…1W4qRnBWAQmjqzoU…5U6sbve9
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.

1.967 Γ— 10⁹²(93-digit number)
19672660355712187943…05703768571040983760
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
1.967 Γ— 10⁹²(93-digit number)
19672660355712187943…05703768571040983759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.967 Γ— 10⁹²(93-digit number)
19672660355712187943…05703768571040983761
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
3.934 Γ— 10⁹²(93-digit number)
39345320711424375886…11407537142081967519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.934 Γ— 10⁹²(93-digit number)
39345320711424375886…11407537142081967521
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
7.869 Γ— 10⁹²(93-digit number)
78690641422848751773…22815074284163935039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.869 Γ— 10⁹²(93-digit number)
78690641422848751773…22815074284163935041
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
1.573 Γ— 10⁹³(94-digit number)
15738128284569750354…45630148568327870079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.573 Γ— 10⁹³(94-digit number)
15738128284569750354…45630148568327870081
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
3.147 Γ— 10⁹³(94-digit number)
31476256569139500709…91260297136655740159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.147 Γ— 10⁹³(94-digit number)
31476256569139500709…91260297136655740161
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
6.295 Γ— 10⁹³(94-digit number)
62952513138279001418…82520594273311480319
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 2772961

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 714f53ab4603174d844617ae7de4b46f60b9c9dd012ab427439182c95ef10418

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 #2,772,961 on Chainz β†—
Circulating Supply:57,940,881 XPMΒ·at block #6,837,071 Β· updates every 60s
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