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Block #55,723

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/17/2013, 3:28:12 AM Β· Difficulty 8.9439 Β· 6,758,405 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a1d07b843c6471a5b9e9322026971a14d01b5e07c8aa8a7e6309c857e192d314
View on Chainz β†—

Height

#55,723

Difficulty

8.943914

Transactions

1

Size

197 B

Version

2

Bits

08f1a453

Nonce

671

Timestamp

7/17/2013, 3:28:12 AM

Confirmations

6,758,405

Merkle Root

1cf47f28ac763b64e43239c193c406529022e65907fba291c850f6e66ed581e9
Transactions (1)
Coinbase1cf47f28ac763b…50f6e66ed581e9
1 in β†’ 1 out12.4800 XPM110 B
AGSjYxN2…CKZEJJvp
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.

1.817 Γ— 10⁸⁷(88-digit number)
18179860026686101630…21840675464701532700
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
1.817 Γ— 10⁸⁷(88-digit number)
18179860026686101630…21840675464701532699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.817 Γ— 10⁸⁷(88-digit number)
18179860026686101630…21840675464701532701
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
3.635 Γ— 10⁸⁷(88-digit number)
36359720053372203260…43681350929403065399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.635 Γ— 10⁸⁷(88-digit number)
36359720053372203260…43681350929403065401
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
7.271 Γ— 10⁸⁷(88-digit number)
72719440106744406521…87362701858806130799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.271 Γ— 10⁸⁷(88-digit number)
72719440106744406521…87362701858806130801
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
1.454 Γ— 10⁸⁸(89-digit number)
14543888021348881304…74725403717612261599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.454 Γ— 10⁸⁸(89-digit number)
14543888021348881304…74725403717612261601
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 55723

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 a1d07b843c6471a5b9e9322026971a14d01b5e07c8aa8a7e6309c857e192d314

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 #55,723 on Chainz β†—
Circulating Supply:57,757,109 XPMΒ·at block #6,814,127 Β· updates every 60s
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