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Home/Chain Registry/Block #1,250,142

Block #1,250,142

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/23/2015, 8:09:52 PM Β· Difficulty 10.7714 Β· 5,576,411 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cdc4b7b11d2d16c118e660583bb0af9cf5fea529dd9dd87e1965102b7c2bc78a
View on Chainz β†—

Difficulty

10.771367

Transactions

1

Size

198 B

Version

2

Bits

0ac57857

Nonce

215,377,480

Timestamp

9/23/2015, 8:09:52 PM

Confirmations

5,576,411

Merkle Root

c9a5637fdb9c8214d8057213267975e27745f8a4b66efe90f78934b5b954b03a
Transactions (1)
Coinbasec9a5637fdb9c82…8934b5b954b03a
1 in β†’ 1 out8.6100 XPM109 B
AP65EmZJ…ScbaX8tp
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.

1.082 Γ— 10⁹³(94-digit number)
10822224017694866844…00066351891855373440
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
1.082 Γ— 10⁹³(94-digit number)
10822224017694866844…00066351891855373439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.082 Γ— 10⁹³(94-digit number)
10822224017694866844…00066351891855373441
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
2.164 Γ— 10⁹³(94-digit number)
21644448035389733688…00132703783710746879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.164 Γ— 10⁹³(94-digit number)
21644448035389733688…00132703783710746881
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
4.328 Γ— 10⁹³(94-digit number)
43288896070779467377…00265407567421493759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.328 Γ— 10⁹³(94-digit number)
43288896070779467377…00265407567421493761
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
8.657 Γ— 10⁹³(94-digit number)
86577792141558934755…00530815134842987519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.657 Γ— 10⁹³(94-digit number)
86577792141558934755…00530815134842987521
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
1.731 Γ— 10⁹⁴(95-digit number)
17315558428311786951…01061630269685975039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.731 Γ— 10⁹⁴(95-digit number)
17315558428311786951…01061630269685975041
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 1250142

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 cdc4b7b11d2d16c118e660583bb0af9cf5fea529dd9dd87e1965102b7c2bc78a

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 #1,250,142 on Chainz β†—
Circulating Supply:57,856,574 XPMΒ·at block #6,826,552 Β· updates every 60s
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