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Block #879,440

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/2/2015, 4:35:21 PM Β· Difficulty 10.9625 Β· 5,953,514 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b76539a7e7b33a0dd8be7dfec6fb69e5a6e4c92aa658d7d3274a246bd63e0000
View on Chainz β†—

Height

#879,440

Difficulty

10.962518

Transactions

1

Size

207 B

Version

2

Bits

0af66791

Nonce

1,620,312,555

Timestamp

1/2/2015, 4:35:21 PM

Confirmations

5,953,514

Merkle Root

98cd552d7de7ce34b83bbca3701963ca43ac2dec4fa581b9abb715a53b3244fb
Transactions (1)
Coinbase98cd552d7de7ce…b715a53b3244fb
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.488 Γ— 10⁹⁷(98-digit number)
24888499742973666719…29492912299584327680
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
2.488 Γ— 10⁹⁷(98-digit number)
24888499742973666719…29492912299584327679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.488 Γ— 10⁹⁷(98-digit number)
24888499742973666719…29492912299584327681
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
4.977 Γ— 10⁹⁷(98-digit number)
49776999485947333438…58985824599168655359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.977 Γ— 10⁹⁷(98-digit number)
49776999485947333438…58985824599168655361
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
9.955 Γ— 10⁹⁷(98-digit number)
99553998971894666876…17971649198337310719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.955 Γ— 10⁹⁷(98-digit number)
99553998971894666876…17971649198337310721
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
1.991 Γ— 10⁹⁸(99-digit number)
19910799794378933375…35943298396674621439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.991 Γ— 10⁹⁸(99-digit number)
19910799794378933375…35943298396674621441
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
3.982 Γ— 10⁹⁸(99-digit number)
39821599588757866750…71886596793349242879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.982 Γ— 10⁹⁸(99-digit number)
39821599588757866750…71886596793349242881
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 879440

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 b76539a7e7b33a0dd8be7dfec6fb69e5a6e4c92aa658d7d3274a246bd63e0000

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 #879,440 on Chainz β†—
Circulating Supply:57,907,811 XPMΒ·at block #6,832,953 Β· updates every 60s
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