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Block #276,270

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 2:37:05 AM Β· Difficulty 9.9628 Β· 6,540,588 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eddab814a8d70a62bbfcc5d7106ebbc98f4f69c740cb4fd9ca5411457cf647c7
View on Chainz β†—

Height

#276,270

Difficulty

9.962785

Transactions

1

Size

236 B

Version

2

Bits

09f67915

Nonce

238

Timestamp

11/27/2013, 2:37:05 AM

Confirmations

6,540,588

Merkle Root

e5664d70f02ff52d01b07513a6f05b4be031ecace4a454adba1ddadd7e6f1bb8
Transactions (1)
Coinbasee5664d70f02ff5…1ddadd7e6f1bb8
1 in β†’ 2 out10.0600 XPM142 B
AKcbk49N…GJbKa7j1AKNbfPoc…jfkpwAyL
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.

1.185 Γ— 10¹⁰⁴(105-digit number)
11851919893016524025…62591637734508168640
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
1.185 Γ— 10¹⁰⁴(105-digit number)
11851919893016524025…62591637734508168639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.185 Γ— 10¹⁰⁴(105-digit number)
11851919893016524025…62591637734508168641
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
2.370 Γ— 10¹⁰⁴(105-digit number)
23703839786033048051…25183275469016337279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.370 Γ— 10¹⁰⁴(105-digit number)
23703839786033048051…25183275469016337281
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
4.740 Γ— 10¹⁰⁴(105-digit number)
47407679572066096102…50366550938032674559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.740 Γ— 10¹⁰⁴(105-digit number)
47407679572066096102…50366550938032674561
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
9.481 Γ— 10¹⁰⁴(105-digit number)
94815359144132192204…00733101876065349119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.481 Γ— 10¹⁰⁴(105-digit number)
94815359144132192204…00733101876065349121
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
1.896 Γ— 10¹⁰⁡(106-digit number)
18963071828826438440…01466203752130698239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.896 Γ— 10¹⁰⁡(106-digit number)
18963071828826438440…01466203752130698241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 276270

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 eddab814a8d70a62bbfcc5d7106ebbc98f4f69c740cb4fd9ca5411457cf647c7

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 #276,270 on Chainz β†—
Circulating Supply:57,778,907 XPMΒ·at block #6,816,857 Β· updates every 60s
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