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Home/Chain Registry/Block #1,185,602

Block #1,185,602

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2015, 10:22:04 AM Β· Difficulty 10.8897 Β· 5,619,445 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
df8a50eaa007cfc90414d9dcf96e68d461ba7f262c6ceecc74d85ad6c1f6160b
View on Chainz β†—

Difficulty

10.889728

Transactions

1

Size

199 B

Version

2

Bits

0ae3c535

Nonce

712,036,837

Timestamp

8/7/2015, 10:22:04 AM

Confirmations

5,619,445

Merkle Root

e682c1bd5688b1519d399e2baf0d712442f27f30998e891ec22d1da904121b8b
Transactions (1)
Coinbasee682c1bd5688b1…2d1da904121b8b
1 in β†’ 1 out8.4200 XPM109 B
Aefu6T1q…v17GNQUY
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.

2.502 Γ— 10⁹⁡(96-digit number)
25020147161527422007…52015102501577221120
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
2.502 Γ— 10⁹⁡(96-digit number)
25020147161527422007…52015102501577221119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.502 Γ— 10⁹⁡(96-digit number)
25020147161527422007…52015102501577221121
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
5.004 Γ— 10⁹⁡(96-digit number)
50040294323054844014…04030205003154442239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.004 Γ— 10⁹⁡(96-digit number)
50040294323054844014…04030205003154442241
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
1.000 Γ— 10⁹⁢(97-digit number)
10008058864610968802…08060410006308884479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.000 Γ— 10⁹⁢(97-digit number)
10008058864610968802…08060410006308884481
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
2.001 Γ— 10⁹⁢(97-digit number)
20016117729221937605…16120820012617768959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.001 Γ— 10⁹⁢(97-digit number)
20016117729221937605…16120820012617768961
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
4.003 Γ— 10⁹⁢(97-digit number)
40032235458443875211…32241640025235537919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.003 Γ— 10⁹⁢(97-digit number)
40032235458443875211…32241640025235537921
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 1185602

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 df8a50eaa007cfc90414d9dcf96e68d461ba7f262c6ceecc74d85ad6c1f6160b

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 #1,185,602 on Chainz β†—
Circulating Supply:57,684,441 XPMΒ·at block #6,805,046 Β· updates every 60s
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