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Home/Chain Registry/Block #2,634,780

Block #2,634,780

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 12:38:42 AM Β· Difficulty 11.2692 Β· 4,195,891 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca769c0f5aadb8c5100de80e47ce070d19bf0eb58ec053c3771b16f1eb8a245f
View on Chainz β†—

Difficulty

11.269173

Transactions

1

Size

200 B

Version

2

Bits

0b44e87f

Nonce

137,121,053

Timestamp

4/29/2018, 12:38:42 AM

Confirmations

4,195,891

Merkle Root

c8f5fea2266fb5f94326ee9c4b1fd5922ead156026c9144b2174a4b5f01e78f6
Transactions (1)
Coinbasec8f5fea2266fb5…74a4b5f01e78f6
1 in β†’ 1 out7.8600 XPM110 B
AaSrKR6E…Qvmpyqn6
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.

3.319 Γ— 10⁹⁡(96-digit number)
33199953051998656775…99943253998845758400
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
3.319 Γ— 10⁹⁡(96-digit number)
33199953051998656775…99943253998845758399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.319 Γ— 10⁹⁡(96-digit number)
33199953051998656775…99943253998845758401
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
6.639 Γ— 10⁹⁡(96-digit number)
66399906103997313550…99886507997691516799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.639 Γ— 10⁹⁡(96-digit number)
66399906103997313550…99886507997691516801
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
1.327 Γ— 10⁹⁢(97-digit number)
13279981220799462710…99773015995383033599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.327 Γ— 10⁹⁢(97-digit number)
13279981220799462710…99773015995383033601
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
2.655 Γ— 10⁹⁢(97-digit number)
26559962441598925420…99546031990766067199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.655 Γ— 10⁹⁢(97-digit number)
26559962441598925420…99546031990766067201
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
5.311 Γ— 10⁹⁢(97-digit number)
53119924883197850840…99092063981532134399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.311 Γ— 10⁹⁢(97-digit number)
53119924883197850840…99092063981532134401
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
1.062 Γ— 10⁹⁷(98-digit number)
10623984976639570168…98184127963064268799
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10623984976639570168…98184127963064268801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2634780

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 ca769c0f5aadb8c5100de80e47ce070d19bf0eb58ec053c3771b16f1eb8a245f

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 #2,634,780 on Chainz β†—
Circulating Supply:57,889,497 XPMΒ·at block #6,830,670 Β· updates every 60s
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