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Home/Chain Registry/Block #2,653,971

Block #2,653,971

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/8/2018, 9:29:52 PM Β· Difficulty 11.7285 Β· 4,190,873 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9f2933e823c7bb499af1f03e5f2de1f11ce8e5a5f6f9c2137577ada7b64335fd
View on Chainz β†—

Difficulty

11.728453

Transactions

1

Size

201 B

Version

2

Bits

0bba7be9

Nonce

319,175,798

Timestamp

5/8/2018, 9:29:52 PM

Confirmations

4,190,873

Merkle Root

46cec7a76a09d6981558e972ae8387bbaf151c90151e117fdf6d25f85628dcd6
Transactions (1)
Coinbase46cec7a76a09d6…6d25f85628dcd6
1 in β†’ 1 out7.2600 XPM110 B
AGNwNKDB…GKxzEnVE
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.

1.017 Γ— 10⁹⁢(97-digit number)
10179963809327996393…70683777069034854400
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
1.017 Γ— 10⁹⁢(97-digit number)
10179963809327996393…70683777069034854399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.017 Γ— 10⁹⁢(97-digit number)
10179963809327996393…70683777069034854401
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
2.035 Γ— 10⁹⁢(97-digit number)
20359927618655992786…41367554138069708799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.035 Γ— 10⁹⁢(97-digit number)
20359927618655992786…41367554138069708801
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
4.071 Γ— 10⁹⁢(97-digit number)
40719855237311985573…82735108276139417599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.071 Γ— 10⁹⁢(97-digit number)
40719855237311985573…82735108276139417601
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
8.143 Γ— 10⁹⁢(97-digit number)
81439710474623971147…65470216552278835199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.143 Γ— 10⁹⁢(97-digit number)
81439710474623971147…65470216552278835201
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
1.628 Γ— 10⁹⁷(98-digit number)
16287942094924794229…30940433104557670399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.628 Γ— 10⁹⁷(98-digit number)
16287942094924794229…30940433104557670401
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
3.257 Γ— 10⁹⁷(98-digit number)
32575884189849588459…61880866209115340799
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.257 Γ— 10⁹⁷(98-digit number)
32575884189849588459…61880866209115340801
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 2653971

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 9f2933e823c7bb499af1f03e5f2de1f11ce8e5a5f6f9c2137577ada7b64335fd

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 #2,653,971 on Chainz β†—
Circulating Supply:58,003,161 XPMΒ·at block #6,844,843 Β· updates every 60s
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