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Home/Chain Registry/Block #2,623,280

Block #2,623,280

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/21/2018, 6:29:27 AM Β· Difficulty 11.2194 Β· 4,214,763 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7a51b564732e39954283ce21ef8edba4d57d76628e67b959f0d6ee16219c9a5e
View on Chainz β†—

Difficulty

11.219405

Transactions

1

Size

201 B

Version

2

Bits

0b382ae7

Nonce

831,199,138

Timestamp

4/21/2018, 6:29:27 AM

Confirmations

4,214,763

Merkle Root

56cabca772e7fe7359e51a85bc7814138df2a5c2bf5ef6bb583477179469a259
Transactions (1)
Coinbase56cabca772e7fe…3477179469a259
1 in β†’ 1 out7.9300 XPM109 B
AKCLu6Jh…huNgs4BF
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.

1.979 Γ— 10⁹⁹(100-digit number)
19793776661854866491…13341893728854343680
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
1.979 Γ— 10⁹⁹(100-digit number)
19793776661854866491…13341893728854343679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.979 Γ— 10⁹⁹(100-digit number)
19793776661854866491…13341893728854343681
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
3.958 Γ— 10⁹⁹(100-digit number)
39587553323709732982…26683787457708687359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.958 Γ— 10⁹⁹(100-digit number)
39587553323709732982…26683787457708687361
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
7.917 Γ— 10⁹⁹(100-digit number)
79175106647419465964…53367574915417374719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.917 Γ— 10⁹⁹(100-digit number)
79175106647419465964…53367574915417374721
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
1.583 Γ— 10¹⁰⁰(101-digit number)
15835021329483893192…06735149830834749439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.583 Γ— 10¹⁰⁰(101-digit number)
15835021329483893192…06735149830834749441
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
3.167 Γ— 10¹⁰⁰(101-digit number)
31670042658967786385…13470299661669498879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.167 Γ— 10¹⁰⁰(101-digit number)
31670042658967786385…13470299661669498881
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
6.334 Γ— 10¹⁰⁰(101-digit number)
63340085317935572771…26940599323338997759
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 2623280

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 7a51b564732e39954283ce21ef8edba4d57d76628e67b959f0d6ee16219c9a5e

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 #2,623,280 on Chainz β†—
Circulating Supply:57,948,696 XPMΒ·at block #6,838,042 Β· updates every 60s
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