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Block #352,101

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2014, 3:34:02 AM Β· Difficulty 10.3006 Β· 6,462,015 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1cdc2cfc51fe28cf4ac1eb1d961da6adce9ad21c2225a2754bfdd5ea5e050da8
View on Chainz β†—

Height

#352,101

Difficulty

10.300614

Transactions

1

Size

207 B

Version

2

Bits

0a4cf507

Nonce

54,033

Timestamp

1/10/2014, 3:34:02 AM

Confirmations

6,462,015

Merkle Root

558b093fe3c9c0bd65091277333c7c8cf63a4123ac2d9ba0ad85c1e8e446e8d7
Transactions (1)
Coinbase558b093fe3c9c0…85c1e8e446e8d7
1 in β†’ 1 out9.4100 XPM116 B
AbwWkWZt…kawDhufa
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.

3.830 Γ— 10⁹⁷(98-digit number)
38308142704373232244…39339425362746943720
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
3.830 Γ— 10⁹⁷(98-digit number)
38308142704373232244…39339425362746943719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.830 Γ— 10⁹⁷(98-digit number)
38308142704373232244…39339425362746943721
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
7.661 Γ— 10⁹⁷(98-digit number)
76616285408746464488…78678850725493887439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.661 Γ— 10⁹⁷(98-digit number)
76616285408746464488…78678850725493887441
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
1.532 Γ— 10⁹⁸(99-digit number)
15323257081749292897…57357701450987774879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.532 Γ— 10⁹⁸(99-digit number)
15323257081749292897…57357701450987774881
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
3.064 Γ— 10⁹⁸(99-digit number)
30646514163498585795…14715402901975549759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.064 Γ— 10⁹⁸(99-digit number)
30646514163498585795…14715402901975549761
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
6.129 Γ— 10⁹⁸(99-digit number)
61293028326997171590…29430805803951099519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.129 Γ— 10⁹⁸(99-digit number)
61293028326997171590…29430805803951099521
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 352101

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 1cdc2cfc51fe28cf4ac1eb1d961da6adce9ad21c2225a2754bfdd5ea5e050da8

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 #352,101 on Chainz β†—
Circulating Supply:57,757,011 XPMΒ·at block #6,814,115 Β· updates every 60s
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