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Block #140,715

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2013, 8:15:53 PM Β· Difficulty 9.8339 Β· 6,684,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
08b68a26e55f26cf0cc936dc6bd09b4b347b02ff2b861abd3e373f6250eafca0
View on Chainz β†—

Height

#140,715

Difficulty

9.833880

Transactions

2

Size

3.20 KB

Version

2

Bits

09d57924

Nonce

210,373

Timestamp

8/29/2013, 8:15:53 PM

Confirmations

6,684,111

Merkle Root

9b35993203265ed68df13bf5a5e3241fdb9a8b2b956b2b92cf41bf4d6a0e58fc
Transactions (2)
Coinbaseef9458fb2ad6f5…0569a9e905bf65
1 in β†’ 1 out10.3700 XPM109 B
AP3eEdAa…a8ZPu6bG
e8e4b7ac0f2c7e…cbeb866bda5c51
26 in β†’ 2 out259.0102 XPM3.00 KB
ATgTXu3k…iLAydbkpAK3BPWdV…Z24cphA1
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.

1.144 Γ— 10⁹⁡(96-digit number)
11448003645068967789…49605023760364648960
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
1.144 Γ— 10⁹⁡(96-digit number)
11448003645068967789…49605023760364648959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.144 Γ— 10⁹⁡(96-digit number)
11448003645068967789…49605023760364648961
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
2.289 Γ— 10⁹⁡(96-digit number)
22896007290137935579…99210047520729297919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.289 Γ— 10⁹⁡(96-digit number)
22896007290137935579…99210047520729297921
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
4.579 Γ— 10⁹⁡(96-digit number)
45792014580275871159…98420095041458595839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.579 Γ— 10⁹⁡(96-digit number)
45792014580275871159…98420095041458595841
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
9.158 Γ— 10⁹⁡(96-digit number)
91584029160551742318…96840190082917191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.158 Γ— 10⁹⁡(96-digit number)
91584029160551742318…96840190082917191681
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
1.831 Γ— 10⁹⁢(97-digit number)
18316805832110348463…93680380165834383359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.831 Γ— 10⁹⁢(97-digit number)
18316805832110348463…93680380165834383361
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 140715

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 08b68a26e55f26cf0cc936dc6bd09b4b347b02ff2b861abd3e373f6250eafca0

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 #140,715 on Chainz β†—
Circulating Supply:57,842,687 XPMΒ·at block #6,824,825 Β· updates every 60s
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