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Block #902,341

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/20/2015, 6:52:04 AM Β· Difficulty 10.9402 Β· 5,894,273 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a7f0b451c9cd3e155a11f0c709d9d24513fcc131f0fc34a7f69da5ff941f6eae
View on Chainz β†—

Height

#902,341

Difficulty

10.940188

Transactions

1

Size

200 B

Version

2

Bits

0af0b029

Nonce

57,593,371

Timestamp

1/20/2015, 6:52:04 AM

Confirmations

5,894,273

Merkle Root

ccaa6555760e815438c06a75f2da422d0cb6597eb8417189487e54aa1b28557e
Transactions (1)
Coinbaseccaa6555760e81…7e54aa1b28557e
1 in β†’ 1 out8.3400 XPM110 B
AVdsvsQP…Uahh8by2
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.

1.058 Γ— 10⁹⁡(96-digit number)
10580306816443788632…70635029869011817920
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
1.058 Γ— 10⁹⁡(96-digit number)
10580306816443788632…70635029869011817919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.058 Γ— 10⁹⁡(96-digit number)
10580306816443788632…70635029869011817921
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
2.116 Γ— 10⁹⁡(96-digit number)
21160613632887577264…41270059738023635839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.116 Γ— 10⁹⁡(96-digit number)
21160613632887577264…41270059738023635841
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
4.232 Γ— 10⁹⁡(96-digit number)
42321227265775154528…82540119476047271679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.232 Γ— 10⁹⁡(96-digit number)
42321227265775154528…82540119476047271681
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
8.464 Γ— 10⁹⁡(96-digit number)
84642454531550309056…65080238952094543359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.464 Γ— 10⁹⁡(96-digit number)
84642454531550309056…65080238952094543361
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
1.692 Γ— 10⁹⁢(97-digit number)
16928490906310061811…30160477904189086719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.692 Γ— 10⁹⁢(97-digit number)
16928490906310061811…30160477904189086721
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 902341

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 a7f0b451c9cd3e155a11f0c709d9d24513fcc131f0fc34a7f69da5ff941f6eae

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 #902,341 on Chainz β†—
Circulating Supply:57,616,909 XPMΒ·at block #6,796,613 Β· updates every 60s
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