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Block #321,506

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2013, 9:06:50 AM Β· Difficulty 10.1896 Β· 6,503,140 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ce902269ec00227667fdcbb19140ff41024f729cef9aebef07e7342c7cebe86b
View on Chainz β†—

Height

#321,506

Difficulty

10.189573

Transactions

1

Size

207 B

Version

2

Bits

0a3087e1

Nonce

83,888,573

Timestamp

12/20/2013, 9:06:50 AM

Confirmations

6,503,140

Merkle Root

04698fabd03e594a22dc224f66af6c5d837775dbf89d626f1fcf2bd6f23124cd
Transactions (1)
Coinbase04698fabd03e59…cf2bd6f23124cd
1 in β†’ 1 out9.6200 XPM116 B
AbwWkWZt…kawDhufa
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.

6.342 Γ— 10⁹⁷(98-digit number)
63424049162890644968…53662921983058027520
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
6.342 Γ— 10⁹⁷(98-digit number)
63424049162890644968…53662921983058027519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.342 Γ— 10⁹⁷(98-digit number)
63424049162890644968…53662921983058027521
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
1.268 Γ— 10⁹⁸(99-digit number)
12684809832578128993…07325843966116055039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.268 Γ— 10⁹⁸(99-digit number)
12684809832578128993…07325843966116055041
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
2.536 Γ— 10⁹⁸(99-digit number)
25369619665156257987…14651687932232110079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.536 Γ— 10⁹⁸(99-digit number)
25369619665156257987…14651687932232110081
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
5.073 Γ— 10⁹⁸(99-digit number)
50739239330312515974…29303375864464220159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.073 Γ— 10⁹⁸(99-digit number)
50739239330312515974…29303375864464220161
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
1.014 Γ— 10⁹⁹(100-digit number)
10147847866062503194…58606751728928440319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.014 Γ— 10⁹⁹(100-digit number)
10147847866062503194…58606751728928440321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 321506

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 ce902269ec00227667fdcbb19140ff41024f729cef9aebef07e7342c7cebe86b

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 #321,506 on Chainz β†—
Circulating Supply:57,841,232 XPMΒ·at block #6,824,645 Β· updates every 60s
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