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Home/Chain Registry/Block #2,698,753

Block #2,698,753

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 6/9/2018, 10:22:00 PM Β· Difficulty 11.6468 Β· 4,141,695 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef72e4920da77cc08391ea2b5c556f731503b00a6ed51cda15402c48f5c21a8b
View on Chainz β†—

Difficulty

11.646798

Transactions

1

Size

201 B

Version

2

Bits

0ba59493

Nonce

810,928,323

Timestamp

6/9/2018, 10:22:00 PM

Confirmations

4,141,695

Merkle Root

ade60d28edce492f873b5821ca51a324bd069924c6c228e259396bcfb8a53eb7
Transactions (1)
Coinbaseade60d28edce49…396bcfb8a53eb7
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
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.

6.784 Γ— 10⁹⁡(96-digit number)
67845174073817940181…81628174557765784320
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
6.784 Γ— 10⁹⁡(96-digit number)
67845174073817940181…81628174557765784319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.784 Γ— 10⁹⁡(96-digit number)
67845174073817940181…81628174557765784321
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
1.356 Γ— 10⁹⁢(97-digit number)
13569034814763588036…63256349115531568639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.356 Γ— 10⁹⁢(97-digit number)
13569034814763588036…63256349115531568641
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
2.713 Γ— 10⁹⁢(97-digit number)
27138069629527176072…26512698231063137279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.713 Γ— 10⁹⁢(97-digit number)
27138069629527176072…26512698231063137281
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
5.427 Γ— 10⁹⁢(97-digit number)
54276139259054352145…53025396462126274559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.427 Γ— 10⁹⁢(97-digit number)
54276139259054352145…53025396462126274561
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
1.085 Γ— 10⁹⁷(98-digit number)
10855227851810870429…06050792924252549119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.085 Γ— 10⁹⁷(98-digit number)
10855227851810870429…06050792924252549121
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
2.171 Γ— 10⁹⁷(98-digit number)
21710455703621740858…12101585848505098239
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.171 Γ— 10⁹⁷(98-digit number)
21710455703621740858…12101585848505098241
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 2698753

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 ef72e4920da77cc08391ea2b5c556f731503b00a6ed51cda15402c48f5c21a8b

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 #2,698,753 on Chainz β†—
Circulating Supply:57,967,914 XPMΒ·at block #6,840,447 Β· updates every 60s
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