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Block #55,119

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/17/2013, 12:04:11 AM Β· Difficulty 8.9393 Β· 6,759,705 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef35cc3361229530424e26be3cc27587fdc7ae9a294da982dae88e42f4193dd7
View on Chainz β†—

Height

#55,119

Difficulty

8.939271

Transactions

1

Size

203 B

Version

2

Bits

08f0740a

Nonce

598

Timestamp

7/17/2013, 12:04:11 AM

Confirmations

6,759,705

Merkle Root

26096b3ff63d385187a488589fa42679de3b11ddfa78f4d9ff459cf9a991c35e
Transactions (1)
Coinbase26096b3ff63d38…459cf9a991c35e
1 in β†’ 1 out12.5000 XPM110 B
AKF9GJzR…PU4pnp3L
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.

5.505 Γ— 10¹⁰²(103-digit number)
55057099752408734109…72006469225012330460
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
5.505 Γ— 10¹⁰²(103-digit number)
55057099752408734109…72006469225012330459
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.505 Γ— 10¹⁰²(103-digit number)
55057099752408734109…72006469225012330461
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
1.101 Γ— 10¹⁰³(104-digit number)
11011419950481746821…44012938450024660919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.101 Γ— 10¹⁰³(104-digit number)
11011419950481746821…44012938450024660921
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
2.202 Γ— 10¹⁰³(104-digit number)
22022839900963493643…88025876900049321839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.202 Γ— 10¹⁰³(104-digit number)
22022839900963493643…88025876900049321841
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
4.404 Γ— 10¹⁰³(104-digit number)
44045679801926987287…76051753800098643679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.404 Γ— 10¹⁰³(104-digit number)
44045679801926987287…76051753800098643681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 55119

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 ef35cc3361229530424e26be3cc27587fdc7ae9a294da982dae88e42f4193dd7

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 #55,119 on Chainz β†—
Circulating Supply:57,762,680 XPMΒ·at block #6,814,823 Β· updates every 60s
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