XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #120,289

Block #120,289

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/17/2013, 1:53:44 AM Β· Difficulty 9.7498 Β· 6,696,487 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2beba38ea989d01ca6563db1f9fe50c165c271b5a2cbc4c6edc8a9401bfca18
View on Chainz β†—

Height

#120,289

Difficulty

9.749801

Transactions

1

Size

200 B

Version

2

Bits

09bff2ef

Nonce

347,733

Timestamp

8/17/2013, 1:53:44 AM

Confirmations

6,696,487

Merkle Root

ad1a81a34fc3221219a6c6caff73d86a4a41c9897d32856dac22d2fcc1af0f82
Transactions (1)
Coinbasead1a81a34fc322…22d2fcc1af0f82
1 in β†’ 1 out10.5000 XPM109 B
AHTcTaqW…MFb3V4Cb
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.

7.386 Γ— 10⁹⁷(98-digit number)
73867925516526906953…41242625169122701600
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
7.386 Γ— 10⁹⁷(98-digit number)
73867925516526906953…41242625169122701599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.386 Γ— 10⁹⁷(98-digit number)
73867925516526906953…41242625169122701601
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
1.477 Γ— 10⁹⁸(99-digit number)
14773585103305381390…82485250338245403199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.477 Γ— 10⁹⁸(99-digit number)
14773585103305381390…82485250338245403201
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
2.954 Γ— 10⁹⁸(99-digit number)
29547170206610762781…64970500676490806399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.954 Γ— 10⁹⁸(99-digit number)
29547170206610762781…64970500676490806401
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
5.909 Γ— 10⁹⁸(99-digit number)
59094340413221525562…29941001352981612799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.909 Γ— 10⁹⁸(99-digit number)
59094340413221525562…29941001352981612801
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
1.181 Γ— 10⁹⁹(100-digit number)
11818868082644305112…59882002705963225599
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 120289

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 b2beba38ea989d01ca6563db1f9fe50c165c271b5a2cbc4c6edc8a9401bfca18

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 #120,289 on Chainz β†—
Circulating Supply:57,778,242 XPMΒ·at block #6,816,775 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy