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Home/Chain Registry/Block #1,170,351

Block #1,170,351

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2015, 10:17:15 PM Β· Difficulty 10.9357 Β· 5,657,016 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd08e767d617e5f3a6a71b7bb65502a4ccdd1ba532a13f3cd2b477681dfb5d98
View on Chainz β†—

Difficulty

10.935703

Transactions

1

Size

200 B

Version

2

Bits

0aef8a3b

Nonce

1,644,228,304

Timestamp

7/25/2015, 10:17:15 PM

Confirmations

5,657,016

Merkle Root

22f55f9c34d0d2f948a0e26a7aa30e108a1ceac67bbfdb2953dc64a6a66c00fb
Transactions (1)
Coinbase22f55f9c34d0d2…dc64a6a66c00fb
1 in β†’ 1 out8.3500 XPM109 B
AVQVsJtD…1QrLiRgQ
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.

3.203 Γ— 10⁹⁷(98-digit number)
32038351017365270166…40792195640639488000
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
3.203 Γ— 10⁹⁷(98-digit number)
32038351017365270166…40792195640639487999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.203 Γ— 10⁹⁷(98-digit number)
32038351017365270166…40792195640639488001
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
6.407 Γ— 10⁹⁷(98-digit number)
64076702034730540333…81584391281278975999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.407 Γ— 10⁹⁷(98-digit number)
64076702034730540333…81584391281278976001
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
1.281 Γ— 10⁹⁸(99-digit number)
12815340406946108066…63168782562557951999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.281 Γ— 10⁹⁸(99-digit number)
12815340406946108066…63168782562557952001
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
2.563 Γ— 10⁹⁸(99-digit number)
25630680813892216133…26337565125115903999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.563 Γ— 10⁹⁸(99-digit number)
25630680813892216133…26337565125115904001
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
5.126 Γ— 10⁹⁸(99-digit number)
51261361627784432266…52675130250231807999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.126 Γ— 10⁹⁸(99-digit number)
51261361627784432266…52675130250231808001
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
1.025 Γ— 10⁹⁹(100-digit number)
10252272325556886453…05350260500463615999
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 1170351

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 fd08e767d617e5f3a6a71b7bb65502a4ccdd1ba532a13f3cd2b477681dfb5d98

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 #1,170,351 on Chainz β†—
Circulating Supply:57,863,037 XPMΒ·at block #6,827,366 Β· updates every 60s
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