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Home/Chain Registry/Block #2,460,272

Block #2,460,272

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2018, 2:19:42 PM Β· Difficulty 10.9545 Β· 4,383,698 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6953325a983ecdb06f4cd4ec230daebdc87d1a1bfd959138000f8fbd00c479ac
View on Chainz β†—

Difficulty

10.954484

Transactions

1

Size

201 B

Version

2

Bits

0af45909

Nonce

1,239,503,672

Timestamp

1/6/2018, 2:19:42 PM

Confirmations

4,383,698

Merkle Root

d9cdf50cfb9e02527a46c1a1fe4649d58f6525639c18801f055577accd0311e9
Transactions (1)
Coinbased9cdf50cfb9e02…5577accd0311e9
1 in β†’ 1 out8.3200 XPM110 B
AWg7ugBu…EXXdUpzg
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.

7.008 Γ— 10⁹⁷(98-digit number)
70080859313129730343…57088830393633792000
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
7.008 Γ— 10⁹⁷(98-digit number)
70080859313129730343…57088830393633791999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.008 Γ— 10⁹⁷(98-digit number)
70080859313129730343…57088830393633792001
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
1.401 Γ— 10⁹⁸(99-digit number)
14016171862625946068…14177660787267583999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.401 Γ— 10⁹⁸(99-digit number)
14016171862625946068…14177660787267584001
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
2.803 Γ— 10⁹⁸(99-digit number)
28032343725251892137…28355321574535167999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.803 Γ— 10⁹⁸(99-digit number)
28032343725251892137…28355321574535168001
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
5.606 Γ— 10⁹⁸(99-digit number)
56064687450503784275…56710643149070335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.606 Γ— 10⁹⁸(99-digit number)
56064687450503784275…56710643149070336001
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
1.121 Γ— 10⁹⁹(100-digit number)
11212937490100756855…13421286298140671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.121 Γ— 10⁹⁹(100-digit number)
11212937490100756855…13421286298140672001
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
2.242 Γ— 10⁹⁹(100-digit number)
22425874980201513710…26842572596281343999
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 2460272

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 6953325a983ecdb06f4cd4ec230daebdc87d1a1bfd959138000f8fbd00c479ac

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 #2,460,272 on Chainz β†—
Circulating Supply:57,996,138 XPMΒ·at block #6,843,969 Β· updates every 60s
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