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Block #141,290

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2013, 5:15:10 AM Β· Difficulty 9.8350 Β· 6,673,182 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7d859be447ebc59196cc21f2c8a17fa0f153c0036b1edf02c2f70c6525a36dca
View on Chainz β†—

Height

#141,290

Difficulty

9.835031

Transactions

1

Size

198 B

Version

2

Bits

09d5c49b

Nonce

100,390

Timestamp

8/30/2013, 5:15:10 AM

Confirmations

6,673,182

Merkle Root

f00760f396d05448cf7595ee63daa47b5fdbdb6899dcab76e9ff810e27a08ed0
Transactions (1)
Coinbasef00760f396d054…ff810e27a08ed0
1 in β†’ 1 out10.3200 XPM109 B
AQ9FGFAJ…CAyw6yEq
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.

2.729 Γ— 10⁹³(94-digit number)
27296579121115034714…64675247876216217600
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
2.729 Γ— 10⁹³(94-digit number)
27296579121115034714…64675247876216217599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.729 Γ— 10⁹³(94-digit number)
27296579121115034714…64675247876216217601
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
5.459 Γ— 10⁹³(94-digit number)
54593158242230069428…29350495752432435199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.459 Γ— 10⁹³(94-digit number)
54593158242230069428…29350495752432435201
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
1.091 Γ— 10⁹⁴(95-digit number)
10918631648446013885…58700991504864870399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.091 Γ— 10⁹⁴(95-digit number)
10918631648446013885…58700991504864870401
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
2.183 Γ— 10⁹⁴(95-digit number)
21837263296892027771…17401983009729740799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.183 Γ— 10⁹⁴(95-digit number)
21837263296892027771…17401983009729740801
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
4.367 Γ— 10⁹⁴(95-digit number)
43674526593784055542…34803966019459481599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.367 Γ— 10⁹⁴(95-digit number)
43674526593784055542…34803966019459481601
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 141290

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 7d859be447ebc59196cc21f2c8a17fa0f153c0036b1edf02c2f70c6525a36dca

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 #141,290 on Chainz β†—
Circulating Supply:57,759,850 XPMΒ·at block #6,814,471 Β· updates every 60s
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