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Block #280,967

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2013, 8:55:49 PM Β· Difficulty 9.9759 Β· 6,531,827 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f7c0ee69ecff4e8fd42c1819fe138234e7a9ab12b593ecd22c8fda804f2fe21f
View on Chainz β†—

Height

#280,967

Difficulty

9.975879

Transactions

1

Size

201 B

Version

2

Bits

09f9d33b

Nonce

68,086

Timestamp

11/28/2013, 8:55:49 PM

Confirmations

6,531,827

Merkle Root

73bb4c5605a48b1743f28b5a7fc8ced4b1a1ce632cb886854da071dc18306950
Transactions (1)
Coinbase73bb4c5605a48b…a071dc18306950
1 in β†’ 1 out10.0300 XPM109 B
AYEzJq7k…7DzDky4R
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.

4.754 Γ— 10¹⁰⁰(101-digit number)
47548192525812383282…73496114534289404000
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
4.754 Γ— 10¹⁰⁰(101-digit number)
47548192525812383282…73496114534289403999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.754 Γ— 10¹⁰⁰(101-digit number)
47548192525812383282…73496114534289404001
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
9.509 Γ— 10¹⁰⁰(101-digit number)
95096385051624766564…46992229068578807999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.509 Γ— 10¹⁰⁰(101-digit number)
95096385051624766564…46992229068578808001
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
1.901 Γ— 10¹⁰¹(102-digit number)
19019277010324953312…93984458137157615999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.901 Γ— 10¹⁰¹(102-digit number)
19019277010324953312…93984458137157616001
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
3.803 Γ— 10¹⁰¹(102-digit number)
38038554020649906625…87968916274315231999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.803 Γ— 10¹⁰¹(102-digit number)
38038554020649906625…87968916274315232001
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
7.607 Γ— 10¹⁰¹(102-digit number)
76077108041299813251…75937832548630463999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.607 Γ— 10¹⁰¹(102-digit number)
76077108041299813251…75937832548630464001
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 280967

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 f7c0ee69ecff4e8fd42c1819fe138234e7a9ab12b593ecd22c8fda804f2fe21f

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 #280,967 on Chainz β†—
Circulating Supply:57,746,394 XPMΒ·at block #6,812,793 Β· updates every 60s
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