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Block #106,147

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2013, 9:28:47 PM Β· Difficulty 9.5996 Β· 6,710,072 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
de05dda4c159d4d742b9b671711971114e40e54d7725296265e5e9d501d1331c
View on Chainz β†—

Height

#106,147

Difficulty

9.599587

Transactions

2

Size

357 B

Version

2

Bits

09997e8b

Nonce

59,086

Timestamp

8/8/2013, 9:28:47 PM

Confirmations

6,710,072

Merkle Root

6685c84b3381c97c5f71469e60281a9f9fae9d66f2eca886a5e6f74510df5ea3
Transactions (2)
Coinbase6bcb391f39151c…6d56646520f54b
1 in β†’ 1 out10.8500 XPM109 B
AeEXQxqG…J2q5dxWc
0909bc02b09409…9c81028f2bd030
1 in β†’ 1 out11.0300 XPM158 B
AQj5CF31…Sfv2KzXY
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.

1.970 Γ— 10⁹⁡(96-digit number)
19709447955213942740…92711410657742336540
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
1.970 Γ— 10⁹⁡(96-digit number)
19709447955213942740…92711410657742336539
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.970 Γ— 10⁹⁡(96-digit number)
19709447955213942740…92711410657742336541
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
3.941 Γ— 10⁹⁡(96-digit number)
39418895910427885481…85422821315484673079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.941 Γ— 10⁹⁡(96-digit number)
39418895910427885481…85422821315484673081
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
7.883 Γ— 10⁹⁡(96-digit number)
78837791820855770962…70845642630969346159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.883 Γ— 10⁹⁡(96-digit number)
78837791820855770962…70845642630969346161
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
1.576 Γ— 10⁹⁢(97-digit number)
15767558364171154192…41691285261938692319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.576 Γ— 10⁹⁢(97-digit number)
15767558364171154192…41691285261938692321
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
3.153 Γ— 10⁹⁢(97-digit number)
31535116728342308384…83382570523877384639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 106147

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 de05dda4c159d4d742b9b671711971114e40e54d7725296265e5e9d501d1331c

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 #106,147 on Chainz β†—
Circulating Supply:57,773,881 XPMΒ·at block #6,816,218 Β· updates every 60s
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