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Block #273,947

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/26/2013, 1:42:04 AM Β· Difficulty 9.9561 Β· 6,527,959 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
411a1a63329e7a1d54be4f65d26517b3491a5d1a0fa304506f7abd3a5304db1e
View on Chainz β†—

Height

#273,947

Difficulty

9.956074

Transactions

1

Size

207 B

Version

2

Bits

09f4c145

Nonce

763

Timestamp

11/26/2013, 1:42:04 AM

Confirmations

6,527,959

Merkle Root

391737e4d77f51fada074e7d91635148ab0473658a0c58ceff71757c3560cbd8
Transactions (1)
Coinbase391737e4d77f51…71757c3560cbd8
1 in β†’ 1 out10.0700 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.520 Γ— 10⁹⁢(97-digit number)
85203018373219937960…30777097252397253760
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
8.520 Γ— 10⁹⁢(97-digit number)
85203018373219937960…30777097252397253759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.520 Γ— 10⁹⁢(97-digit number)
85203018373219937960…30777097252397253761
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
1.704 Γ— 10⁹⁷(98-digit number)
17040603674643987592…61554194504794507519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.704 Γ— 10⁹⁷(98-digit number)
17040603674643987592…61554194504794507521
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
3.408 Γ— 10⁹⁷(98-digit number)
34081207349287975184…23108389009589015039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.408 Γ— 10⁹⁷(98-digit number)
34081207349287975184…23108389009589015041
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
6.816 Γ— 10⁹⁷(98-digit number)
68162414698575950368…46216778019178030079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.816 Γ— 10⁹⁷(98-digit number)
68162414698575950368…46216778019178030081
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
1.363 Γ— 10⁹⁸(99-digit number)
13632482939715190073…92433556038356060159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 273947

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 411a1a63329e7a1d54be4f65d26517b3491a5d1a0fa304506f7abd3a5304db1e

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 #273,947 on Chainz β†—
Circulating Supply:57,659,342 XPMΒ·at block #6,801,905 Β· updates every 60s
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