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Home/Chain Registry/Block #2,415,918

Block #2,415,918

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2017, 7:59:17 AM Β· Difficulty 10.9041 Β· 4,429,023 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06ef71224198b2b644121e916a46877a5016c5b810ff4c7867d0fd5ecba96c10
View on Chainz β†—

Difficulty

10.904110

Transactions

1

Size

200 B

Version

2

Bits

0ae773be

Nonce

1,580,687,450

Timestamp

12/9/2017, 7:59:17 AM

Confirmations

4,429,023

Merkle Root

69be90bd7a8d50a685c8b97d8ebd29c2f0bafd343939f7c657402f087a2e76b6
Transactions (1)
Coinbase69be90bd7a8d50…402f087a2e76b6
1 in β†’ 1 out8.4000 XPM110 B
AYweB36k…gLLM4nT6
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.

4.330 Γ— 10⁹⁴(95-digit number)
43308500377134475053…30213100158958690080
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
4.330 Γ— 10⁹⁴(95-digit number)
43308500377134475053…30213100158958690079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.330 Γ— 10⁹⁴(95-digit number)
43308500377134475053…30213100158958690081
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
8.661 Γ— 10⁹⁴(95-digit number)
86617000754268950106…60426200317917380159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.661 Γ— 10⁹⁴(95-digit number)
86617000754268950106…60426200317917380161
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
1.732 Γ— 10⁹⁡(96-digit number)
17323400150853790021…20852400635834760319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.732 Γ— 10⁹⁡(96-digit number)
17323400150853790021…20852400635834760321
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
3.464 Γ— 10⁹⁡(96-digit number)
34646800301707580042…41704801271669520639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.464 Γ— 10⁹⁡(96-digit number)
34646800301707580042…41704801271669520641
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
6.929 Γ— 10⁹⁡(96-digit number)
69293600603415160085…83409602543339041279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.929 Γ— 10⁹⁡(96-digit number)
69293600603415160085…83409602543339041281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁢(97-digit number)
13858720120683032017…66819205086678082559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2415918

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 06ef71224198b2b644121e916a46877a5016c5b810ff4c7867d0fd5ecba96c10

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 #2,415,918 on Chainz β†—
Circulating Supply:58,003,947 XPMΒ·at block #6,844,940 Β· updates every 60s
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