XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,176,968

Block #2,176,968

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 7:24:52 AM Β· Difficulty 10.9215 Β· 4,664,437 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e344ea6f33af9028e32e6c63381ddf60c3eeceabaf3908f3e5aefdc779ce22ac
View on Chainz β†—

Difficulty

10.921450

Transactions

2

Size

870 B

Version

2

Bits

0aebe42c

Nonce

1,960,867,887

Timestamp

6/25/2017, 7:24:52 AM

Confirmations

4,664,437

Merkle Root

d9d1f7068af323440e528452d7b933f594f4bda681f1b92a2789ee3d93a2ff68
Transactions (2)
Coinbasebccacd9522a40f…e0c191f4c34ef4
1 in β†’ 1 out8.3800 XPM110 B
AUU5bhX5…g3uWdFeM
90ea43cba042e8…6f94113014ef29
4 in β†’ 2 out12.9900 XPM670 B
AYmFscQ3…yE7JKc2sATiHcXmR…xJrHDJQS
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.

7.427 Γ— 10⁹⁴(95-digit number)
74270966493771295309…43242870828744486000
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
7.427 Γ— 10⁹⁴(95-digit number)
74270966493771295309…43242870828744485999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.427 Γ— 10⁹⁴(95-digit number)
74270966493771295309…43242870828744486001
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
1.485 Γ— 10⁹⁡(96-digit number)
14854193298754259061…86485741657488971999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.485 Γ— 10⁹⁡(96-digit number)
14854193298754259061…86485741657488972001
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
2.970 Γ— 10⁹⁡(96-digit number)
29708386597508518123…72971483314977943999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.970 Γ— 10⁹⁡(96-digit number)
29708386597508518123…72971483314977944001
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
5.941 Γ— 10⁹⁡(96-digit number)
59416773195017036247…45942966629955887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.941 Γ— 10⁹⁡(96-digit number)
59416773195017036247…45942966629955888001
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
1.188 Γ— 10⁹⁢(97-digit number)
11883354639003407249…91885933259911775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.188 Γ— 10⁹⁢(97-digit number)
11883354639003407249…91885933259911776001
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
2.376 Γ— 10⁹⁢(97-digit number)
23766709278006814499…83771866519823551999
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 2176968

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 e344ea6f33af9028e32e6c63381ddf60c3eeceabaf3908f3e5aefdc779ce22ac

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 #2,176,968 on Chainz β†—
Circulating Supply:57,975,614 XPMΒ·at block #6,841,404 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