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Home/Chain Registry/Block #1,250,852

Block #1,250,852

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2015, 6:29:29 AM Β· Difficulty 10.7754 Β· 5,544,365 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f488d4b984f37e4e466022dd6e69dc5ded842e9483bf98a4029539098e21c437
View on Chainz β†—

Difficulty

10.775385

Transactions

1

Size

201 B

Version

2

Bits

0ac67f9d

Nonce

1,834,672,081

Timestamp

9/24/2015, 6:29:29 AM

Confirmations

5,544,365

Merkle Root

df09cddbf4b3730e0d1f1c4eddb652e2596e7d96e361749a78c58bce12ac0e33
Transactions (1)
Coinbasedf09cddbf4b373…c58bce12ac0e33
1 in β†’ 1 out8.6000 XPM110 B
AThRRB14…Yhsxnkt1
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.

1.724 Γ— 10⁹⁸(99-digit number)
17241866636325137655…78370193856013271040
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
1.724 Γ— 10⁹⁸(99-digit number)
17241866636325137655…78370193856013271039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.724 Γ— 10⁹⁸(99-digit number)
17241866636325137655…78370193856013271041
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
3.448 Γ— 10⁹⁸(99-digit number)
34483733272650275311…56740387712026542079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.448 Γ— 10⁹⁸(99-digit number)
34483733272650275311…56740387712026542081
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
6.896 Γ— 10⁹⁸(99-digit number)
68967466545300550623…13480775424053084159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.896 Γ— 10⁹⁸(99-digit number)
68967466545300550623…13480775424053084161
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
1.379 Γ— 10⁹⁹(100-digit number)
13793493309060110124…26961550848106168319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.379 Γ— 10⁹⁹(100-digit number)
13793493309060110124…26961550848106168321
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
2.758 Γ— 10⁹⁹(100-digit number)
27586986618120220249…53923101696212336639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.758 Γ— 10⁹⁹(100-digit number)
27586986618120220249…53923101696212336641
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 1250852

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 f488d4b984f37e4e466022dd6e69dc5ded842e9483bf98a4029539098e21c437

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 #1,250,852 on Chainz β†—
Circulating Supply:57,605,789 XPMΒ·at block #6,795,216 Β· updates every 60s
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