XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,156,713

Block #3,156,713

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2019, 7:43:08 PM Β· Difficulty 11.3209 Β· 3,680,759 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cb0607a0df74111eace4f6e4a7e41fbcf08f0afa8aadb61034cc1897a1d2e086
View on Chainz β†—

Difficulty

11.320928

Transactions

2

Size

3.46 KB

Version

2

Bits

0b522858

Nonce

96,791,754

Timestamp

4/26/2019, 7:43:08 PM

Confirmations

3,680,759

Merkle Root

a496a853f8275f77e6152f53ed4f1bb9dce7208fdf3d45d15ab65954aa5288db
Transactions (2)
Coinbase81ddbc40b632eb…f197137344da3c
1 in β†’ 1 out7.8300 XPM110 B
AbXwmGxD…4XXYP765
d5c124a47ac3ef…6eea678f537d72
22 in β†’ 2 out1040.7562 XPM3.26 KB
Aax7uriG…3VNKEmbPAQpirNZH…YMX3K11g
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.

1.267 Γ— 10⁹⁴(95-digit number)
12676513710114857860…33460871243798092980
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
1.267 Γ— 10⁹⁴(95-digit number)
12676513710114857860…33460871243798092979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.267 Γ— 10⁹⁴(95-digit number)
12676513710114857860…33460871243798092981
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
2.535 Γ— 10⁹⁴(95-digit number)
25353027420229715721…66921742487596185959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.535 Γ— 10⁹⁴(95-digit number)
25353027420229715721…66921742487596185961
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
5.070 Γ— 10⁹⁴(95-digit number)
50706054840459431442…33843484975192371919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.070 Γ— 10⁹⁴(95-digit number)
50706054840459431442…33843484975192371921
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
1.014 Γ— 10⁹⁡(96-digit number)
10141210968091886288…67686969950384743839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.014 Γ— 10⁹⁡(96-digit number)
10141210968091886288…67686969950384743841
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
2.028 Γ— 10⁹⁡(96-digit number)
20282421936183772577…35373939900769487679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.028 Γ— 10⁹⁡(96-digit number)
20282421936183772577…35373939900769487681
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
4.056 Γ— 10⁹⁡(96-digit number)
40564843872367545154…70747879801538975359
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 3156713

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 cb0607a0df74111eace4f6e4a7e41fbcf08f0afa8aadb61034cc1897a1d2e086

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 #3,156,713 on Chainz β†—
Circulating Supply:57,944,097 XPMΒ·at block #6,837,471 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