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Block #2,636,504

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 2:54:47 PM Β· Difficulty 11.3849 Β· 4,204,576 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
97eee7729ab0d3f52d391aef6b87bed0202bc890b68fa41c4ae294a9863f762f
View on Chainz β†—

Difficulty

11.384902

Transactions

1

Size

201 B

Version

2

Bits

0b6288f0

Nonce

513,861,420

Timestamp

4/29/2018, 2:54:47 PM

Confirmations

4,204,576

Merkle Root

0441156525a232ffc27dc738708b55ceca2106e607709d1c43fcc5a7c8d49b0b
Transactions (1)
Coinbase0441156525a232…fcc5a7c8d49b0b
1 in β†’ 1 out7.7000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.259 Γ— 10⁹⁷(98-digit number)
12596197535298310865…29179211249231536640
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
1.259 Γ— 10⁹⁷(98-digit number)
12596197535298310865…29179211249231536639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.259 Γ— 10⁹⁷(98-digit number)
12596197535298310865…29179211249231536641
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
2.519 Γ— 10⁹⁷(98-digit number)
25192395070596621730…58358422498463073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.519 Γ— 10⁹⁷(98-digit number)
25192395070596621730…58358422498463073281
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
5.038 Γ— 10⁹⁷(98-digit number)
50384790141193243460…16716844996926146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.038 Γ— 10⁹⁷(98-digit number)
50384790141193243460…16716844996926146561
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
1.007 Γ— 10⁹⁸(99-digit number)
10076958028238648692…33433689993852293119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10076958028238648692…33433689993852293121
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
2.015 Γ— 10⁹⁸(99-digit number)
20153916056477297384…66867379987704586239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.015 Γ— 10⁹⁸(99-digit number)
20153916056477297384…66867379987704586241
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
4.030 Γ— 10⁹⁸(99-digit number)
40307832112954594768…33734759975409172479
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 2636504

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 97eee7729ab0d3f52d391aef6b87bed0202bc890b68fa41c4ae294a9863f762f

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 #2,636,504 on Chainz β†—
Circulating Supply:57,973,002 XPMΒ·at block #6,841,079 Β· updates every 60s
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