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Block #353,139

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2014, 6:28:04 PM Β· Difficulty 10.3206 Β· 6,442,798 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
57474286a7327f2bfa4a4f48a0b2adfd18bfef8134b4baadf984afe5d02f1621
View on Chainz β†—

Height

#353,139

Difficulty

10.320641

Transactions

1

Size

205 B

Version

2

Bits

0a521581

Nonce

41,922

Timestamp

1/10/2014, 6:28:04 PM

Confirmations

6,442,798

Merkle Root

cd9c739721bc90df2586c76c2adca96bdd4dbba95437d9576b41cb4598b84eec
Transactions (1)
Coinbasecd9c739721bc90…41cb4598b84eec
1 in β†’ 1 out9.3700 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.

2.636 Γ— 10⁹²(93-digit number)
26361261195744244833…97954271867464509010
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
2.636 Γ— 10⁹²(93-digit number)
26361261195744244833…97954271867464509009
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.636 Γ— 10⁹²(93-digit number)
26361261195744244833…97954271867464509011
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
5.272 Γ— 10⁹²(93-digit number)
52722522391488489666…95908543734929018019
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.272 Γ— 10⁹²(93-digit number)
52722522391488489666…95908543734929018021
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
1.054 Γ— 10⁹³(94-digit number)
10544504478297697933…91817087469858036039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.054 Γ— 10⁹³(94-digit number)
10544504478297697933…91817087469858036041
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
2.108 Γ— 10⁹³(94-digit number)
21089008956595395866…83634174939716072079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.108 Γ— 10⁹³(94-digit number)
21089008956595395866…83634174939716072081
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
4.217 Γ— 10⁹³(94-digit number)
42178017913190791733…67268349879432144159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.217 Γ— 10⁹³(94-digit number)
42178017913190791733…67268349879432144161
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 353139

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 57474286a7327f2bfa4a4f48a0b2adfd18bfef8134b4baadf984afe5d02f1621

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 #353,139 on Chainz β†—
Circulating Supply:57,611,585 XPMΒ·at block #6,795,936 Β· updates every 60s
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