XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,761,927

Block #2,761,927

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2018, 5:58:10 PM Β· Difficulty 11.6543 Β· 4,079,187 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
92c31dc8db31e9398f5b97f513ad9c4e6d4cd748d7a5a569c4f863c00cb60820
View on Chainz β†—

Difficulty

11.654345

Transactions

1

Size

198 B

Version

2

Bits

0ba78329

Nonce

2,048,628,726

Timestamp

7/23/2018, 5:58:10 PM

Confirmations

4,079,187

Merkle Root

2d1e719eda65af315b130555625b5ef3218cd6a87969720f76e9144654ab6cc7
Transactions (1)
Coinbase2d1e719eda65af…e9144654ab6cc7
1 in β†’ 1 out7.3500 XPM109 B
AZtxQr2F…7grUWrUz
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.

1.225 Γ— 10⁹³(94-digit number)
12254226150981751069…07731917056972642750
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
1.225 Γ— 10⁹³(94-digit number)
12254226150981751069…07731917056972642749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.225 Γ— 10⁹³(94-digit number)
12254226150981751069…07731917056972642751
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
2.450 Γ— 10⁹³(94-digit number)
24508452301963502139…15463834113945285499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.450 Γ— 10⁹³(94-digit number)
24508452301963502139…15463834113945285501
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
4.901 Γ— 10⁹³(94-digit number)
49016904603927004278…30927668227890570999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.901 Γ— 10⁹³(94-digit number)
49016904603927004278…30927668227890571001
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
9.803 Γ— 10⁹³(94-digit number)
98033809207854008557…61855336455781141999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.803 Γ— 10⁹³(94-digit number)
98033809207854008557…61855336455781142001
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
1.960 Γ— 10⁹⁴(95-digit number)
19606761841570801711…23710672911562283999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.960 Γ— 10⁹⁴(95-digit number)
19606761841570801711…23710672911562284001
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
3.921 Γ— 10⁹⁴(95-digit number)
39213523683141603422…47421345823124567999
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 2761927

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 92c31dc8db31e9398f5b97f513ad9c4e6d4cd748d7a5a569c4f863c00cb60820

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 #2,761,927 on Chainz β†—
Circulating Supply:57,973,279 XPMΒ·at block #6,841,113 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy