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Home/Chain Registry/Block #1,150,839

Block #1,150,839

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2015, 6:08:38 PM Β· Difficulty 10.9456 Β· 5,674,807 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2a0716cfb58af2d1c1194a9aeac134b8be9304c91eeeccc460ea84df7b33ec66
View on Chainz β†—

Difficulty

10.945625

Transactions

1

Size

206 B

Version

2

Bits

0af2147f

Nonce

292,156,601

Timestamp

7/11/2015, 6:08:38 PM

Confirmations

5,674,807

Merkle Root

73cd4fc5f576cfd26cdbc2be3bffd2abddd471916a91dea3944111d54e651d9e
Transactions (1)
Coinbase73cd4fc5f576cf…4111d54e651d9e
1 in β†’ 1 out8.3300 XPM116 B
AJCEY9yy…tg97E6zm
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.

1.587 Γ— 10⁹⁡(96-digit number)
15879207522135809426…02399771390048221000
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
1.587 Γ— 10⁹⁡(96-digit number)
15879207522135809426…02399771390048220999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.587 Γ— 10⁹⁡(96-digit number)
15879207522135809426…02399771390048221001
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
3.175 Γ— 10⁹⁡(96-digit number)
31758415044271618853…04799542780096441999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.175 Γ— 10⁹⁡(96-digit number)
31758415044271618853…04799542780096442001
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
6.351 Γ— 10⁹⁡(96-digit number)
63516830088543237707…09599085560192883999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.351 Γ— 10⁹⁡(96-digit number)
63516830088543237707…09599085560192884001
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
1.270 Γ— 10⁹⁢(97-digit number)
12703366017708647541…19198171120385767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.270 Γ— 10⁹⁢(97-digit number)
12703366017708647541…19198171120385768001
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
2.540 Γ— 10⁹⁢(97-digit number)
25406732035417295083…38396342240771535999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.540 Γ— 10⁹⁢(97-digit number)
25406732035417295083…38396342240771536001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.081 Γ— 10⁹⁢(97-digit number)
50813464070834590166…76792684481543071999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1150839

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 2a0716cfb58af2d1c1194a9aeac134b8be9304c91eeeccc460ea84df7b33ec66

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 #1,150,839 on Chainz β†—
Circulating Supply:57,849,273 XPMΒ·at block #6,825,645 Β· updates every 60s
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