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Home/Chain Registry/Block #2,460,371

Block #2,460,371

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 1/6/2018, 4:02:12 PM Β· Difficulty 10.9545 Β· 4,382,701 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
710873dbfcee593f11745c2d1fb9155ccf5bf3a839e554aa6f5eb51ccc24a216
View on Chainz β†—

Difficulty

10.954459

Transactions

2

Size

539 B

Version

2

Bits

0af45771

Nonce

15,013,481

Timestamp

1/6/2018, 4:02:12 PM

Confirmations

4,382,701

Merkle Root

836c44d8e1e73d385c8077765dadbde198ceacf76f5736d3ffb750b118443aa8
Transactions (2)
Coinbasef397e0d94ec8f2…81ecaf63ffd268
1 in β†’ 1 out8.3300 XPM109 B
AacNuMh4…8ZEFvvK7
36f907dbe1136b…b15bcdd184f3c1
2 in β†’ 2 out10.4775 XPM340 B
AJ4TdpG5…GYqxzL2NAGwDiNL3…PZTVeiw5
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.

2.643 Γ— 10⁹⁡(96-digit number)
26439500023438253247…91588848792288716800
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
2.643 Γ— 10⁹⁡(96-digit number)
26439500023438253247…91588848792288716799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.643 Γ— 10⁹⁡(96-digit number)
26439500023438253247…91588848792288716801
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
5.287 Γ— 10⁹⁡(96-digit number)
52879000046876506494…83177697584577433599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.287 Γ— 10⁹⁡(96-digit number)
52879000046876506494…83177697584577433601
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
1.057 Γ— 10⁹⁢(97-digit number)
10575800009375301298…66355395169154867199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10575800009375301298…66355395169154867201
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
2.115 Γ— 10⁹⁢(97-digit number)
21151600018750602597…32710790338309734399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.115 Γ— 10⁹⁢(97-digit number)
21151600018750602597…32710790338309734401
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
4.230 Γ— 10⁹⁢(97-digit number)
42303200037501205195…65421580676619468799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.230 Γ— 10⁹⁢(97-digit number)
42303200037501205195…65421580676619468801
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
8.460 Γ— 10⁹⁢(97-digit number)
84606400075002410391…30843161353238937599
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.460 Γ— 10⁹⁢(97-digit number)
84606400075002410391…30843161353238937601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2460371

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 710873dbfcee593f11745c2d1fb9155ccf5bf3a839e554aa6f5eb51ccc24a216

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 #2,460,371 on Chainz β†—
Circulating Supply:57,988,935 XPMΒ·at block #6,843,071 Β· updates every 60s
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