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Block #53,320

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 2:45:41 PM Β· Difficulty 8.9223 Β· 6,747,218 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
779c4cd6658aed1b596423dab62627f7f50ffe5202b1e7c8b9a09fd3055aed18
View on Chainz β†—

Height

#53,320

Difficulty

8.922251

Transactions

1

Size

205 B

Version

2

Bits

08ec18a0

Nonce

40

Timestamp

7/16/2013, 2:45:41 PM

Confirmations

6,747,218

Merkle Root

3385d2e8cdc88eac59479ea87aef7763391db871868c260e371d4853dc0df0ed
Transactions (1)
Coinbase3385d2e8cdc88e…1d4853dc0df0ed
1 in β†’ 1 out12.5400 XPM110 B
AYLhWkmm…N5ssgFep
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.

5.100 Γ— 10¹⁰⁷(108-digit number)
51002549776243025810…35501230593113222000
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
5.100 Γ— 10¹⁰⁷(108-digit number)
51002549776243025810…35501230593113221999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.100 Γ— 10¹⁰⁷(108-digit number)
51002549776243025810…35501230593113222001
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
1.020 Γ— 10¹⁰⁸(109-digit number)
10200509955248605162…71002461186226443999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.020 Γ— 10¹⁰⁸(109-digit number)
10200509955248605162…71002461186226444001
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
2.040 Γ— 10¹⁰⁸(109-digit number)
20401019910497210324…42004922372452887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.040 Γ— 10¹⁰⁸(109-digit number)
20401019910497210324…42004922372452888001
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
4.080 Γ— 10¹⁰⁸(109-digit number)
40802039820994420648…84009844744905775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.080 Γ— 10¹⁰⁸(109-digit number)
40802039820994420648…84009844744905776001
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
8.160 Γ— 10¹⁰⁸(109-digit number)
81604079641988841296…68019689489811551999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 53320

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 779c4cd6658aed1b596423dab62627f7f50ffe5202b1e7c8b9a09fd3055aed18

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 #53,320 on Chainz β†—
Circulating Supply:57,648,366 XPMΒ·at block #6,800,537 Β· updates every 60s
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